D₂₅×C₄₀₁ #34095322

order	20050
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₀₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₂₅×C₄₀₁
unambiguous semidirect product	C₂₅⋊(C₂×C₄₀₁)

Splittings

Fitting, Hall	C₂₅×C₄₀₁ ⋊ C₂
derived, Sylow	C₂₅ ⋊ C₂×C₄₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₀₁	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₄₀₁
Frattini	C₅	D₅×C₄₀₁
Fitting	C₂₅×C₄₀₁	C₂
socle	C₅×C₄₀₁	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₄₀₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 426
transitive degree	μ_t(G) = 10025

A minimal faithful permutation representation — 2 generators on 426 points:

(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,18)(12,20)(14,22)(17,23)(19,24)(21,25)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426);(1,6,21,20,4,3,14,24,10,9,8,23,18,11,17,16,15,5,19,22,7,2,12,25,13)

Conjugacy classes & character table

5614 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20050, 4);

D25×C401 #34095322