C₃₇×#3518 #17992336

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3518

Subgroups

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

1010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8413, C₃₇×#17654, C₃₇×#17683, …
maximal normal subgroup of	C₃₇×#8413, C₃₇×#17654, C₃₇×#17683, …
maximal quotient of	C₃₇×#34193, C₃₇×#34231, C₃₇×#34242, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2250);

C37×#3518 #17992336