C₃₇×#3011 #17991829

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3008
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#3011

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×2₋¹⁺⁴×C₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×#41×C₃₇ ◁ G

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 4 generators on 73 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)(40,41)(42,43,47,51)(44,52,55,65)(45,49,56,63)(46,58,60,50)(48,59,62,54)(53,66,67,73)(57,70,69,64)(61,71,72,68);(42,44,47,55)(43,48,51,62)(45,53,56,67)(46,59,60,54)(49,61,63,72)(50,65,58,52)(57,71,69,68)(64,73,70,66);(39,41)(42,45)(43,49)(44,53)(46,57)(47,56)(48,61)(50,64)(51,63)(52,66)(54,68)(55,67)(58,70)(59,71)(60,69)(62,72)(65,73);(45,56)(49,63)(53,67)(57,69)(61,72)(64,70)(66,73)(68,71)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#13096, C₃₇×#13101, C₃₇×#23893, …
maximal normal subgroup of	C₃₇×#13096, C₃₇×#13101, C₃₇×#23893, …
maximal quotient of	C₃₇×#18227, C₃₇×#18235, C₃₇×#18243, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1743);

C37×#3011 #17991829