C₃₇×#3538 #17992356

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

Aliases

direct product

C₃₇×#3538

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
prime radical	C₃₇×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1014 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)(46,47,51,53)(48,54,56,49)(50,58,59,52)(55,57,61,60);(39,42)(43,45)(46,48,51,56)(47,49,53,54)(50,55,59,61)(52,57,58,60);(38,39)(40,43)(41,42)(44,45);(38,40)(39,43)(41,44)(42,45)(46,49)(47,48)(50,57)(51,54)(52,55)(53,56)(58,61)(59,60);(46,50,51,59)(47,52,53,58)(48,55,56,61)(49,57,54,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8482, C₃₇×#12757, C₃₇×#18230, …
maximal normal subgroup of	C₃₇×#8482, C₃₇×#12757, C₃₇×#18230, …
maximal quotient of	C₃₇×#34360, C₃₇×#34380, C₃₇×#34412, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2270);

C37×#3538 #17992356