C₃₇×#3231 #17992049

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

Aliases

direct product

C₃₇×#3231

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂³×C₃₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

326 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)(54,55,59,62)(56,63,65,68)(57,61,58,66)(60,67,69,64);(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51);(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52)(54,56)(55,60)(57,64)(58,67)(59,65)(61,68)(62,69)(63,66);(39,45)(43,46)(44,53)(51,52)(54,57,59,58)(55,61,62,66)(56,64,65,67)(60,68,69,63)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9280, C₃₇×#9286, C₃₇×#18765, …
maximal normal subgroup of	C₃₇×#9280, C₃₇×#9286, C₃₇×#18765, …
maximal quotient of	C₃₇×#21835, C₃₇×#21864, C₃₇×#21984, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1963);

C37×#3231 #17992049