C₃₇×#3228 #17992046

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3186
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₃₇×#3228

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₃₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#9279, C₃₇×#9284, C₃₇×#18764, …
maximal normal subgroup of	C₃₇×#9279, C₃₇×#9284, C₃₇×#18764, …
maximal quotient of	C₃₇×#21835, C₃₇×#21863, C₃₇×#21984, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1960);

C37×#3228 #17992046