D₃₇×C₁₇₉ #27210387

order	13246
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃₇×C₁₇₉
unambiguous semidirect product	C₃₇⋊(C₂×C₁₇₉)

Splittings

Fitting, socle, Hall	C₃₇×C₁₇₉ ⋊ C₂
derived, Sylow	C₃₇ ⋊ C₂×C₁₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇₉	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂×C₁₇₉
Frattini	C₁	G
Fitting, socle	C₃₇×C₁₇₉	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₁₇₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 216
transitive degree	μ_t(G) = 6623

A minimal faithful permutation representation — 2 generators on 216 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)

Conjugacy classes & character table

3580 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#3866×C₁₇₉, C₁₇₉⋊#3866, D₃₇×D₁₇₉, …
maximal normal subgroup of	#3866×C₁₇₉, C₁₇₉⋊#3866, D₃₇×D₁₇₉, …
maximal quotient of	Dic₃₇×C₁₇₉, C₂×D₃₇×C₁₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13246, 1);

D37×C179 #27210387