C₃₇×#3562 #17992380

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

Aliases

direct product

C₃₇×#3562

Subgroups

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

1050 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)(48,51)(49,54)(50,55)(52,56)(53,58)(57,59)(60,61);(39,42)(43,45)(47,48)(49,56)(53,55)(57,61);(38,39)(40,43)(41,42)(44,45)(46,48,51,47)(49,54,56,52)(50,55,58,53)(57,60,61,59);(38,40,41,44)(39,43,42,45)(46,49)(47,52)(48,54)(50,57)(51,56)(53,59)(55,60)(58,61);(46,50,51,58)(47,53,48,55)(49,57,56,61)(52,59,54,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#62011, C₃₇×#62012, C₃₇×#62013, …
maximal normal subgroup of	C₃₇×#62011, C₃₇×#62012, C₃₇×#62013, …
maximal quotient of	C₃₇×#34385, C₃₇×#34392, C₃₇×#34402, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2294);

C37×#3562 #17992380