C₃₇×#3063 #17991881

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3063

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

472 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)(42,43,47,51)(44,52,54,55)(45,49,48,57)(46,53,56,50);(42,44,46,49,47,54,56,57)(43,48,50,52,51,45,53,55);(39,41)(42,45)(43,49)(44,53)(46,55)(47,48)(50,54)(51,57)(52,56);(44,54)(45,48)(49,57)(52,55)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#25190, C₃₇×#25191, C₃₇×#25194, …
maximal normal subgroup of	C₃₇×#25190, C₃₇×#25191, C₃₇×#25194, …
maximal quotient of	C₃₇×#19231, C₃₇×#19233, C₃₇×#19235, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1795);

C37×#3063 #17991881