C₃₇×#3036 #17991854

order	4736
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#3036

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 49 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)(39,41)(42,43)(44,46)(45,47)(48,49);(38,39,40,41);(43,46)(44,49)(47,48);(43,47)(46,48)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#9179, C₃₇×#9181, C₃₇×#9305, …
maximal normal subgroup of	C₃₇×#9179, C₃₇×#9181, C₃₇×#9305, …
maximal quotient of	C₃₇×#19254, C₃₇×#19255, C₃₇×#19256, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1768);

C37×#3036 #17991854