C₃₇×#3537 #17992355

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3537

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 5 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)(40,44)(41,43)(42,45)(47,50)(48,52);(38,39,41,43)(40,42,45,44)(46,47,49,50)(48,51,52,53);(46,47)(48,51)(49,50)(52,53);(38,39)(40,42)(41,43)(44,45)(46,47)(48,51)(49,50)(52,53);(38,40,41,45)(39,42,43,44)(46,48,49,52)(47,51,50,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8479, C₃₇×#12755, C₃₇×#18228, …
maximal normal subgroup of	C₃₇×#8479, C₃₇×#12755, C₃₇×#18228, …
maximal quotient of	C₃₇×#34360, C₃₇×#34379, C₃₇×#34411, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2269);

C37×#3537 #17992355