C₃₇×#3156 #17991974

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₃₇×#3156

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
prime radical	C₂×#135×C₃₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ #117×C₃₇ ◁ G

532 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)(39,41)(42,43,47,51)(44,52,56,66)(45,49,57,63)(46,59,53,50)(48,60,62,55)(54,65,68,73)(58,70,67,64)(61,71,72,69);(42,44,53,60,47,56,46,55)(43,48,59,66,51,62,50,52)(45,54,67,71,57,68,58,69)(49,61,70,73,63,72,64,65);(38,39,40,41)(42,45)(43,49)(44,54)(46,58)(47,57)(48,61)(50,64)(51,63)(52,65)(53,67)(55,69)(56,68)(59,70)(60,71)(62,72)(66,73);(45,57)(49,63)(54,68)(58,67)(61,72)(64,70)(65,73)(69,71)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#13216, C₃₇×#13335, C₃₇×#13337, …
maximal normal subgroup of	C₃₇×#13216, C₃₇×#13335, C₃₇×#13337, …
maximal quotient of	C₃₇×#19624, C₃₇×#19628, C₃₇×#19630, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1888);

C37×#3156 #17991974