C₃₇×#2564 #17991382

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

Aliases

direct product

C₃₇×#2564

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

584 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)(39,41)(42,43,46,47)(44,45,48,49)(51,52)(53,57);(43,47)(44,48)(50,51,54,52)(53,55,57,56);(38,39,40,41)(42,44)(43,45)(46,48)(47,49)(50,52,54,51)(53,56,57,55);(42,45)(43,44)(46,49)(47,48)(50,53)(51,55)(52,56)(54,57)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9383, C₃₇×#9385, C₃₇×#11789, …
maximal normal subgroup of	C₃₇×#9383, C₃₇×#9385, C₃₇×#11789, …
maximal quotient of	C₃₇×#13908, C₃₇×#13960, C₃₇×#13975, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1296);

C37×#2564 #17991382