C₃₇×#2110 #17990928

order	4736
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2110

Subgroups

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

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(38,39,41,45,42,47,53,61,43,46,54,60,55,62,68,69)(40,48,50,64,51,57,66,59,49,63,52,67,65,44,56,58);(38,40)(39,44,46,57)(41,52)(42,51)(43,49)(45,59,60,58)(47,48,62,63)(50,54)(53,56)(55,65)(61,67,69,64)(66,68);(40,49)(44,57)(48,63)(50,52)(51,65)(56,66)(58,59)(64,67)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#11912, C₃₇×#11913, C₃₇×#11914, …
maximal normal subgroup of	C₃₇×#11912, C₃₇×#11913, C₃₇×#11914, …
maximal quotient of	C₃₇×#11405, C₃₇×#11406, C₃₇×#11413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 842);

C37×#2110 #17990928