C₃₇×#3507 #17992325

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

Aliases

direct product

C₃₇×#3507

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
prime radical	C₃₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1012 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)(40,44)(42,45)(46,47)(48,55)(49,50)(51,52)(53,58)(54,59)(56,61)(57,60);(38,39,41,43)(40,42,44,45)(47,52)(49,54)(53,55)(56,60);(38,40,41,44)(39,42,43,45)(46,48,51,58)(47,53,52,55)(49,56,54,60)(50,57,59,61);(46,49,51,54)(47,50,52,59)(48,56,58,60)(53,57,55,61);(46,50)(47,54)(48,57)(49,52)(51,59)(53,60)(55,56)(58,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8357, C₃₇×#8431, C₃₇×#8435, …
maximal normal subgroup of	C₃₇×#8357, C₃₇×#8431, C₃₇×#8435, …
maximal quotient of	C₃₇×#34187, C₃₇×#34206, C₃₇×#34213, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2239);

C37×#3507 #17992325