C₃×C₇⋊D₅₈₁ #37567398

order	24402
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₃×C₇⋊D₅₈₁
unambiguous semidirect product	C₈₃⋊(C₃×C₇⋊D₇)

Splittings

Fitting, socle, Hall	C₃×C₇²×C₈₃ ⋊ C₂
derived, Hall	C₇²×C₈₃ ⋊ C₂×C₃
Hall	C₃×C₈₃ ⋊ C₇⋊D₇
Hall	C₃×C₇² ⋊ D₈₃
Sylow	C₈₃ ⋊ C₃×C₇⋊D₇
Sylow	C₇² ⋊ C₃×D₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₇⋊D₅₈₁
commutator, cosocle, hypocenter	C₇²×C₈₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₈₃	C₂
LCS	G ▷ C₇²×C₈₃
UCS	C₁ ◁ C₃

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 100
transitive degree	μ_t(G) = 12201

A minimal faithful permutation representation — 3 generators on 100 points:

(1,2,3)(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)(88,89)(90,91)(92,93)(95,96)(97,98)(99,100);(4,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6)(94,95,97,99,100,98,96);(87,88,90,92,93,91,89)

Conjugacy classes & character table

6105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24402, 40);

C3×C7⋊D581 #37567398