C₃₇×#2768 #17991586

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2768

Subgroups

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

408 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)(40,42)(41,43)(44,45)(46,47,50,49)(48,52,53,51)(54,55)(56,60)(57,59)(58,61);(39,40)(41,45)(47,49)(51,52)(54,55,57,59)(56,60,61,58);(38,40,42,39)(41,44,45,43)(46,48,50,53)(47,51,49,52)(54,55)(56,58)(57,59)(60,61);(38,41,42,45)(39,43,40,44)(46,49,50,47)(48,52,53,51)(54,56,57,61)(55,58,59,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36748, C₃₇×#36749, C₃₇×#36750, …
maximal normal subgroup of	C₃₇×#36748, C₃₇×#36749, C₃₇×#36750, …
maximal quotient of	C₃₇×#14386, C₃₇×#14392, C₃₇×#14403, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1500);

C37×#2768 #17991586