C₃₇×#1375 #17990193

order	4736
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1375

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₄²
commutator	C₄	C₄×C₈×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
socle	C₂²×C₃₇	#97
prime radical	C₂³×C₃₇	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 2 generators on 57 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)(40,41)(42,43,45,50,46,48,54,55,47,51,53,57,44,49,52,56);(39,41)(43,48,51,49)(45,53)(50,56,57,55)(52,54)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7109, C₃₇×#7116, C₃₇×#7117, …
maximal normal subgroup of	C₃₇×#7109, C₃₇×#7116, C₃₇×#7117, …
maximal quotient of	C₃₇×#7137, C₃₇×#7142, C₃₇×#7145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 107);

C37×#1375 #17990193