C₃₇×#1373 #17990191

order	4736
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#1373

Subgroups

	subgroup	G/H
center	C₈×C₃₇	D₈
commutator	C₈	C₂×C₈×C₃₇
Frattini, cosocle	C₄×C₈	C₂²×C₃₇
socle	C₂×C₃₇	#335
prime radical	C₂²×C₃₇	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₇ ◁ C₂×C₈×C₃₇ ◁ C₄×C₈×C₃₇ ◁ G

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

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7387, C₃₇×#7388, C₃₇×#7447, …
maximal normal subgroup of	C₃₇×#7387, C₃₇×#7388, C₃₇×#7447, …
maximal quotient of	C₃₇×#7100, C₃₇×#7101, C₃₇×#7160, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 105);

C37×#1373 #17990191