C₂⁵×#90673 #28407571

order	14464
isoclinism	isoclinic class of #90673
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁵

Aliases

direct product	C₂⁵×#90673
unambiguous semidirect product	D₁₁₃⋊(C₂⁴×C₄)

Splittings

Fitting, socle	C₂⁵×C₁₁₃ ⋊ C₄
derived, Sylow	C₁₁₃ ⋊ C₂⁵×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂⁵	#90673
commutator, hypocenter	C₁₁₃	C₂⁵×C₄
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₁₃	C₄
prime radical	C₂⁵×D₁₁₃	C₂
cosocle	D₁₁₃	C₂⁶
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂⁵

10552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 3616

A minimal faithful permutation representation — 6 generators on 123 points:

(12,13,14,16)(15,18,19,25)(17,22,23,21)(20,27,28,38)(24,31,32,34)(26,35,36,30)(29,40,41,55)(33,44,45,51)(37,48,49,47)(39,52,53,43)(42,57,58,76)(46,61,62,72)(50,65,66,68)(54,69,70,64)(56,73,74,60)(59,78,79,101)(63,82,83,97)(67,86,87,93)(71,90,91,89)(75,94,95,85)(77,98,99,81)(80,103,104,108)(84,106,107,122)(88,110,111,120)(92,114,115,117)(96,118,119,113)(100,121,116,109)(102,123,112,105);(9,10)(11,12,15,20,29,42,59,80,103,107,83,62,45,32,23,16,21,30,43,60,81,105,106,78,102,111,87,66,49,36,25,34,47,64,85,109,110,82,57,77,100,115,91,70,53,38,51,68,89,113,114,86,61,40,56,75,96,119,95,74,55,72,93,117,118,90,65,44,27,39,54,71,92,116,99,76,97,120,121,94,69,48,31,18,26,37,50,67,88,112,101,122,123,98,73,52,35,22,13,17,24,33,46,63,84,108,104,79,58,41,28,19,14);(7,8);(5,6);(3,4);(1,2)

Conjugacy classes & character table

1024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21507);

C25×#90673 #28407571