C₃₇×#3390 #17992208

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3390

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄×Q₈×C₃₇ ◁ G

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 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)(38,39,42,41)(40,44,45,43)(46,47)(48,55)(49,53)(50,58)(51,54)(52,57)(56,61)(59,60);(38,40,42,45)(39,43,41,44)(48,56)(52,60)(55,61)(57,59);(46,48,51,56)(47,52,54,60)(49,57,50,59)(53,61,58,55);(38,41,42,39)(40,43,45,44)(46,49,51,50)(47,53,54,58)(48,57,56,59)(52,61,60,55)

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12361, C₃₇×#12363, C₃₇×#12413, …
maximal normal subgroup of	C₃₇×#12361, C₃₇×#12363, C₃₇×#12413, …
maximal quotient of	C₃₇×#22527, C₃₇×#22675, C₃₇×#22679, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2122);

C37×#3390 #17992208