C₃₇×#1369 #17990187

order	4736
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#1369

Subgroups

	subgroup	G/H
center	C₄×C₃₇	#106
commutator	C₈	C₂×C₈×C₃₇
Frattini, cosocle	C₄×C₈	C₂²×C₃₇
socle	C₂×C₃₇	#334
prime radical	C₂²×C₃₇	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂×C₈×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7390, C₃₇×#7391, C₃₇×#7457, …
maximal normal subgroup of	C₃₇×#7390, C₃₇×#7391, C₃₇×#7457, …
maximal quotient of	C₃₇×#7099, C₃₇×#7161, C₂×C₃₇×#1369

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 101);

C37×#1369 #17990187