C₃₇×#1726 #17990544

order	4736
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄³×C₃₇ · Schur multiplier (H₂) = C₂×C₄²

Aliases

direct product

C₃₇×#1726

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₃₇	C₂²
commutator	C₂	C₄³×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle, prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₃₇ ◁ G

328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(46,47,49,52,50,53,56,59)(48,51,55,58,54,57,60,61);(38,39,40,41)(46,48)(47,51)(49,55)(50,54)(52,58)(53,57)(56,60)(59,61);(42,43,44,45)(48,54)(51,57)(55,60)(58,61)

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7150, C₃₇×#8137, C₃₇×#8138, …
maximal normal subgroup of	C₃₇×#7150, C₃₇×#8137, C₃₇×#8138, …
maximal quotient of	C₈×#97×C₃₇, C₃₇×#7841, C₃₇×#7842, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 458);

C37×#1726 #17990544