C₃₇×#3356 #17992174

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3356

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×D₄×C₃₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×D₄×C₃₇ ◁ G

342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,42,41)(40,44,45,43)(46,47,49,53)(48,55,56,51)(50,52,58,54)(57,59,61,60);(38,40)(39,43)(41,44)(42,45)(46,48,49,56)(47,51,53,55)(50,57,58,61)(52,60,54,59);(38,41,42,39)(40,44,45,43)(47,52)(48,56)(50,58)(51,59)(53,54)(55,60);(40,45)(43,44)(47,53)(48,56)(52,54)(57,61)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#19865, C₃₇×#19866, C₃₇×#19881, …
maximal normal subgroup of	C₃₇×#19865, C₃₇×#19866, C₃₇×#19881, …
maximal quotient of	C₃₇×#22502, C₃₇×#22504, C₃₇×#22623, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2088);

C37×#3356 #17992174