C₃₇×#2584 #17991402

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

Aliases

direct product

C₃₇×#2584

Subgroups

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

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 4736

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#10007, C₃₇×#10011, C₃₇×#18277, …
maximal normal subgroup of	C₃₇×#10007, C₃₇×#10011, C₃₇×#18277, …
maximal quotient of	C₃₇×#13925, C₃₇×#13954, C₃₇×#14045, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1316);

C37×#2584 #17991402