C₃₇×#2563 #17991381

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₇×#2563

Subgroups

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

564 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)(42,43,45,46)(44,48,49,47)(51,53)(52,56);(43,46)(47,48)(50,51,54,53)(52,55,56,57);(38,39)(40,41)(42,43)(44,47)(45,46)(48,49)(50,52)(51,55)(53,57)(54,56);(42,44,45,49)(43,47,46,48)(50,53,54,51)(52,57,56,55)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9391, C₃₇×#9399, C₃₇×#9453, …
maximal normal subgroup of	C₃₇×#9391, C₃₇×#9399, C₃₇×#9453, …
maximal quotient of	C₃₇×#13906, C₃₇×#13911, C₃₇×#13973, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1295);

C37×#2563 #17991381