C₃₇×#2528 #17991346

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2528

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

364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 generators on 61 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)(38,39,41,43)(40,42,44,45)(48,52)(51,53)(55,59)(57,61);(38,39,41,43)(40,42,44,45)(46,47,50,49)(48,51,52,53)(54,55,58,59)(56,57,60,61);(38,39)(40,42)(41,43)(44,45)(46,48)(47,51)(49,53)(50,52)(54,56,58,60)(55,57,59,61);(38,40,41,44)(39,42,43,45)(46,49,50,47)(48,53,52,51)(54,57)(55,60)(56,59)(58,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#2528, C₃₇×#34793, C₃₇×#34808, …
maximal normal subgroup of	C₂×C₃₇×#2528, C₃₇×#34793, C₃₇×#34808, …
maximal quotient of	C₃₇×#13897, C₃₇×#13945, C₃₇×#14009, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1260);

C37×#2528 #17991346