C₃₇×#2061 #17990879

order	4736
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2061

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
prime radical	C₂³×C₃₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

230 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1184

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

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#7442, C₃₇×#12235, C₃₇×#12237, …
maximal normal subgroup of	C₃₇×#7442, C₃₇×#12235, C₃₇×#12237, …
maximal quotient of	C₃₇×#10568, C₃₇×#10569, C₃₇×#10571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 793);