C₃₁×D₇₃ #17985348

order	4526
isoclinism	isoclinic class of D₇₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×D₇₃
unambiguous semidirect product	C₇₃⋊(C₂×C₃₁)

Splittings

Fitting, socle, Hall	C₃₁×C₇₃ ⋊ C₂
derived, Sylow	C₇₃ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	D₇₃
commutator, cosocle, hypocenter	C₇₃	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₃₁×C₇₃	C₂
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₃₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 104
transitive degree	μ_t(G) = 2263

A minimal faithful permutation representation — 2 generators on 104 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)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104);(33,104)(34,103)(35,102)(36,101)(37,100)(38,99)(39,98)(40,97)(41,96)(42,95)(43,94)(44,93)(45,92)(46,91)(47,90)(48,89)(49,88)(50,87)(51,86)(52,85)(53,84)(54,83)(55,82)(56,81)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70)(68,69)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₃₁×D₇₃, C₃₁×D₂₁₉, C₃₁×D₇₃⋊C₃, …
maximal normal subgroup of	C₃×C₃₁×D₇₃, C₃₁×D₇₃⋊C₃, C₃₁⋊C₃×D₇₃, …
maximal quotient of	C₃×C₃₁×D₇₃, C₃₁×D₂₁₉, C₅×C₃₁×D₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4526, 2);

C31×D73 #17985348