C₃₇×#3082 #17991900

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3082

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂³×C₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ #117×C₃₇ ◁ G

362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#26401, C₃₇×#26403, C₃₇×#26404, …
maximal normal subgroup of	C₃₇×#26401, C₃₇×#26403, C₃₇×#26404, …
maximal quotient of	C₃₇×#20651, C₃₇×#20877, C₃₇×#20880, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1814);

C37×#3082 #17991900