C₃₇×#1385 #17990203

order	4736
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₄²×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1385

Subgroups

	subgroup	G/H
center	C₄×C₃₇	#106
commutator	C₈	C₄²×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
socle	C₂×C₃₇	#340
prime radical	C₂³×C₃₇	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

124 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)(38,39,42,48,45,50,44,60)(40,51,53,66,55,67,58,62)(41,49,43,59,57,65,56,47)(46,54,61,52,64,68,63,69);(38,40,43,54,42,58,57,69,45,55,56,68,44,53,41,52)(39,46,49,62,60,61,47,51,50,64,65,66,48,63,59,67)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7424, C₃₇×#7425, C₂×C₃₇×#1385, …
maximal normal subgroup of	C₃₇×#7424, C₃₇×#7425, C₂×C₃₇×#1385, …
maximal quotient of	C₃₇×#7157, C₃₇×#7173, C₃₇×#7220, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 117);

C37×#1385 #17990203