C₃₇×#2183 #17991001

order	4736
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#2183

Subgroups

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

126 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)(40,45)(41,43)(42,44)(46,47,49,53,50,48,55,56,51,54,58,61,59,57,52,60);(38,40,42,41)(39,43,44,45);(38,41,42,40)(39,43,44,45)(46,48,49,56,50,54,55,61,51,57,58,60,59,47,52,53)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7393, C₃₇×#12049, C₃₇×#12051, …
maximal normal subgroup of	C₃₇×#7393, C₃₇×#12049, C₃₇×#12051, …
maximal quotient of	C₃₇×#12662, C₃₇×#12663, C₃₇×#13104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 915);

C37×#2183 #17991001