C₃₇×#3233 #17992051

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

Aliases

direct product

C₃₇×#3233

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	#121×C₃₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 69 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)(40,46)(41,44)(42,45)(43,48)(47,52)(49,51)(50,53)(54,55)(56,64)(57,63)(58,60)(59,62)(61,66)(65,69)(67,68);(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51)(55,60)(56,65)(62,63)(66,67);(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52)(54,56,58,65)(55,61,60,68)(57,66,59,67)(62,64,63,69);(39,45)(43,46)(44,53)(51,52)(54,57,58,59)(55,62,60,63)(56,66,65,67)(61,64,68,69)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#18659, C₃₇×#18661, C₃₇×#18671, …
maximal normal subgroup of	C₃₇×#18659, C₃₇×#18661, C₃₇×#18671, …
maximal quotient of	C₃₇×#21837, C₃₇×#21862, C₃₇×#21985, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1965);

C37×#3233 #17992051