C₃₇×#2509 #17991327

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2509

Subgroups

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

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

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

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#26755, C₃₇×#26759, C₃₇×#26762, …
maximal normal subgroup of	C₃₇×#26755, C₃₇×#26759, C₃₇×#26762, …
maximal quotient of	C₃₇×#13885, C₃₇×#13933, C₃₇×#14006, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1241);

C37×#2509 #17991327