C₃₇×#3212 #17992030

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3186
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₃₇×#3212

Subgroups

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

400 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)(38,39)(40,44)(41,43)(42,45)(46,47)(48,56)(49,55)(50,52)(51,54)(53,58)(57,61)(59,60);(38,40,41,45)(39,42,43,44)(47,52)(48,57)(54,55)(58,59);(40,45)(42,44)(46,48)(47,53)(49,58)(50,57)(51,59)(52,60)(54,56)(55,61);(39,43)(42,44)(46,49,50,51)(47,54,52,55)(48,58,57,59)(53,56,60,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#18658, C₃₇×#18660, C₃₇×#18670, …
maximal normal subgroup of	C₃₇×#18658, C₃₇×#18660, C₃₇×#18670, …
maximal quotient of	C₃₇×#21807, C₃₇×#21862, C₃₇×#21985, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1944);

C37×#3212 #17992030