C₃₇×#2932 #17991750

order	4736
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#2932

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂⁴
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
socle	C₂²×C₃₇	C₂³×C₄
prime radical	C₃₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 57 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)(40,41)(42,43,46,50,47,49,55,56)(44,48,52,45,51,53,57,54);(39,41)(42,44)(43,48)(45,50)(46,52)(47,51)(49,53)(54,56)(55,57);(42,45,46,53,47,54,55,48)(43,44,50,52,49,51,56,57);(43,49)(44,51)(50,56)(52,57)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8878, C₃₇×#8880, C₃₇×#9047, …
maximal normal subgroup of	C₃₇×#8878, C₃₇×#8880, C₃₇×#9047, …
maximal quotient of	C₃₇×#17975, C₃₇×#17976, C₃₇×#17977, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1664);

C37×#2932 #17991750