C₃₇×#3535 #17992353

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

Aliases

direct product

C₃₇×#3535

Subgroups

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

1038 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 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)(39,42)(40,44)(47,51)(48,54)(49,57)(59,61);(39,42)(43,45)(46,47,50,51)(48,55,54,52)(49,53,57,58)(56,61,60,59);(38,39)(40,43)(41,42)(44,45)(46,47)(48,52)(49,53)(50,51)(54,55)(56,59)(57,58)(60,61);(38,40)(39,43)(41,44)(42,45)(46,48,50,54)(47,52,51,55)(49,56,57,60)(53,59,58,61);(46,49)(47,53)(48,56)(50,57)(51,58)(52,59)(54,60)(55,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8488, C₃₇×#18226, C₃₇×#18227, …
maximal normal subgroup of	C₃₇×#8488, C₃₇×#18226, C₃₇×#18227, …
maximal quotient of	C₃₇×#34359, C₃₇×#34376, C₃₇×#34386, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2267);

C37×#3535 #17992353