C₃₇×#1454 #17990272

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃₇×#1454

Subgroups

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

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#1454, C₃₇×#17324, C₃₇×#17326, …
maximal normal subgroup of	C₂×C₃₇×#1454, C₃₇×#17324, C₃₇×#17326, …
maximal quotient of	C₃₇×#7845, C₃₇×#7851, C₃₇×#8135, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 186);

C37×#1454 #17990272