C₃₇×#2241 #17991059

order	4736
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃₇×#2241

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(40,43)(41,42)(44,45)(46,47,53,48)(49,50,59,61)(51,58,54,55)(52,60,57,56);(39,42)(43,45)(46,48,51,59,52,60,50,58,53,47,54,49,57,56,61,55);(38,40,41,44)(39,43,42,45)(46,49,50,48,57,58,51,56,53,59,61,47,52,55,54,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12344, C₃₇×#12345, C₃₇×#12346, …
maximal normal subgroup of	C₃₇×#12344, C₃₇×#12345, C₃₇×#12346, …
maximal quotient of	C₃₇×#12888, C₃₇×#13148, C₃₇×#13203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 973);

C37×#2241 #17991059