C₃₇×#2514 #17991332

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

Aliases

direct product

C₃₇×#2514

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

372 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)(39,41)(40,44)(46,47,51,49)(48,53,52,50)(56,60)(58,61);(38,39,42,41)(40,43,44,45)(46,48)(47,50)(49,53)(51,52)(54,55,57,59)(56,61,60,58);(38,40)(39,43)(41,45)(42,44)(46,49,51,47)(48,53,52,50)(54,56,57,60)(55,58,59,61);(38,41,42,39)(40,45,44,43)(46,50,51,53)(47,52,49,48)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#27063, C₃₇×#27067, C₃₇×#27070, …
maximal normal subgroup of	C₃₇×#27063, C₃₇×#27067, C₃₇×#27070, …
maximal quotient of	C₃₇×#13885, C₃₇×#13921, C₃₇×#13989, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1246);

C37×#2514 #17991332