C₃₇×#3495 #17992313

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

Aliases

direct product

C₃₇×#3495

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

1022 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)(40,44)(42,45)(46,47,51,54)(48,49,56,52)(50,58,59,53)(55,60,61,57);(38,39,41,43)(40,42,44,45)(46,48,51,56)(47,52,54,49)(50,55,59,61)(53,60,58,57);(38,40)(39,42)(41,44)(43,45)(46,49)(47,48)(50,57)(51,52)(53,55)(54,56)(58,61)(59,60);(46,48)(47,49)(50,55)(51,56)(52,54)(53,57)(58,60)(59,61);(46,50,51,59)(47,53,54,58)(48,55,56,61)(49,57,52,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8468, C₃₇×#17605, C₃₇×#17609, …
maximal normal subgroup of	C₃₇×#8468, C₃₇×#17605, C₃₇×#17609, …
maximal quotient of	C₃₇×#34180, C₃₇×#34202, C₃₇×#34203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2227);

C37×#3495 #17992313