C₃₇×#3504 #17992322

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

Aliases

direct product

C₃₇×#3504

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
prime radical	C₂×#41×C₃₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

988 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)(38,39,41,43)(40,44,45,42)(46,47)(48,52)(49,56)(50,51)(53,57)(54,60)(55,58)(59,61);(47,51)(52,58)(53,56)(59,60);(38,40,41,45)(39,42,43,44)(46,48,50,55)(47,52,51,58)(49,54,57,61)(53,59,56,60);(46,47)(48,52)(49,53)(50,51)(54,59)(55,58)(56,57)(60,61);(46,49,50,57)(47,53,51,56)(48,54,55,61)(52,59,58,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8478, C₃₇×#17689, C₃₇×#17692, …
maximal normal subgroup of	C₃₇×#8478, C₃₇×#17689, C₃₇×#17692, …
maximal quotient of	C₃₇×#34184, C₃₇×#34215, C₃₇×#34217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2236);

C37×#3504 #17992322