C₃₇×#2508 #17991326

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₇×#2508

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#26753, C₃₇×#26757, C₃₇×#26760, …
maximal normal subgroup of	C₃₇×#26753, C₃₇×#26757, C₃₇×#26760, …
maximal quotient of	C₃₇×#13885, C₃₇×#13918, C₃₇×#13985, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1240);

C37×#2508 #17991326