C₃₇×#3056 #17991874

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3056

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂³×C₄×C₃₇ ◁ G

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

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)(42,43,46,49)(44,50,51,57)(45,53,54,48)(47,55,56,52);(42,44,45,52,46,51,54,55)(43,47,48,50,49,56,53,57);(39,41);(44,51)(47,56)(50,57)(52,55)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#24413, C₃₇×#24415, C₃₇×#24417, …
maximal normal subgroup of	C₃₇×#24413, C₃₇×#24415, C₃₇×#24417, …
maximal quotient of	C₃₇×#19163, C₃₇×#19165, C₃₇×#19167, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1788);

C37×#3056 #17991874