C₃₇×#1398 #17990216

order	4736
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#1398

Subgroups

	subgroup	G/H
center	C₈×C₃₇	C₄²
commutator	C₄	C₄×C₈×C₃₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₃₇
socle	C₂×C₃₇	#346
prime radical	C₂²×C₃₇	M₃₂
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ 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)(38,39,40,45,41,47,50,60,42,48,51,58,52,62,64,68,43,46,49,59,53,61,63,69,54,44,55,56,65,57,66,67);(39,44,46,48)(40,49)(45,58,59,56)(47,57,61,62)(50,63)(51,55)(60,68,69,67)(64,66)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7333, C₃₇×#7389, C₃₇×#7390, …
maximal normal subgroup of	C₃₇×#7333, C₃₇×#7389, C₃₇×#7390, …
maximal quotient of	C₃₇×#7330, C₃₇×#7332, C₃₇×#7466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 130);

C37×#1398 #17990216