C₃₇×#1422 #17990240

order	4736
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#1422

Subgroups

	subgroup	G/H
center	C₁₆×C₃₇	D₄
commutator	C₄	C₂×C₁₆×C₃₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₃₇
socle	C₂×C₃₇	C₄⋊C₁₆
prime radical	C₂²×C₃₇	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₃₇ ◁ C₂×C₁₆×C₃₇ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 2 generators on 69 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)(38,39,42,48,43,49,57,64,44,47,58,62,54,63,67,69,45,50,59,65,52,46,60,61,41,55,56,68,40,51,53,66);(38,40,41,52,45,54,44,43)(39,46,47,51,50,49,55,63)(42,53,56,60,59,67,58,57)(48,61,62,66,65,64,68,69)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7381, C₃₇×#7382, C₃₇×#7447, …
maximal normal subgroup of	C₃₇×#7381, C₃₇×#7382, C₃₇×#7447, …
maximal quotient of	C₃₇×#7455, C₃₇×#7458, C₃₇×#7467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 154);

C37×#1422 #17990240