C₃₇×#2746 #17991564

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

Aliases

direct product

C₃₇×#2746

Subgroups

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

448 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)(40,44)(41,42)(43,45)(46,47,50,52)(48,53,49,51)(54,55)(56,59)(57,61)(58,60);(39,42)(43,44)(46,48,50,49)(47,51,52,53)(54,56,58,61)(55,59,60,57);(38,40,41,45)(39,43,42,44)(46,49,50,48)(47,51,52,53)(54,56)(55,57)(58,61)(59,60);(38,39)(40,43)(41,42)(44,45)(46,47)(48,53)(49,51)(50,52)(54,57)(55,56)(58,59)(60,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#36726, C₃₇×#36730, C₃₇×#36734, …
maximal normal subgroup of	C₃₇×#36726, C₃₇×#36730, C₃₇×#36734, …
maximal quotient of	C₃₇×#14368, C₃₇×#14371, C₃₇×#14373, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1478);

C37×#2746 #17991564