C₃₇×#2060 #17990878

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

Aliases

direct product

C₃₇×#2060

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

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

normal subgroups only

This group has 246 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) = 53
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 3 generators on 53 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)(48,50)(49,52)(51,53);(38,40,42,41)(39,43,44,45)(48,53)(50,51);(38,41,42,40)(39,43,44,45)(47,50)(48,53)(51,52)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#7443, C₃₇×#12234, C₃₇×#12236, …
maximal normal subgroup of	C₃₇×#7443, C₃₇×#12234, C₃₇×#12236, …
maximal quotient of	C₃₇×#10567, C₃₇×#10570, C₃₇×#10572, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 792);