C₃₇×#2527 #17991345

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×#2527

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

420 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)(38,39,41,43)(40,42,44,45)(46,47)(48,52)(49,51)(50,53)(56,60)(59,61);(38,39,41,43)(40,42,44,45)(46,47,49,51)(48,50,53,52)(54,55,58,57)(56,59,60,61);(38,39)(40,42)(41,43)(44,45)(46,47)(48,50)(49,51)(52,53)(54,56)(55,59)(57,61)(58,60);(38,40,41,44)(39,42,43,45)(46,48)(47,50)(49,53)(51,52)(54,57,58,55)(56,61,60,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#2527, C₃₇×#34803, C₃₇×#34806, …
maximal normal subgroup of	C₂×C₃₇×#2527, C₃₇×#34803, C₃₇×#34806, …
maximal quotient of	C₃₇×#13895, C₃₇×#13946, C₃₇×#14008, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1259);

C37×#2527 #17991345