C₃₇×D₆₄ #17990247

order	4736
nilpotency class	6
isoclinism	isoclinic class of D₆₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×D₆₄

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂²×C₃₇
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₄×C₃₇ ◁ C₈×C₃₇ ◁ C₁₆×C₃₇ ◁ C₃₂×C₃₇ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 2 generators on 101 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)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(39,101)(40,100)(41,99)(42,98)(43,97)(44,96)(45,95)(46,94)(47,93)(48,92)(49,91)(50,90)(51,89)(52,88)(53,87)(54,86)(55,85)(56,84)(57,83)(58,82)(59,81)(60,80)(61,79)(62,78)(63,77)(64,76)(65,75)(66,74)(67,73)(68,72)(69,71)

Conjugacy classes & character table

1295 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×D₁₂₈, C₃₇×SD₂₅₆, C₂×C₃₇×D₆₄, …
maximal normal subgroup of	C₃₇×D₁₂₈, C₃₇×SD₂₅₆, C₂×C₃₇×D₆₄, …
maximal quotient of	C₃₇×#7537, C₃₇×#7545, C₃₇×D₁₂₈, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 161);

C37×D64 #17990247