D₃×#16860688 #37562045

order	23994
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#16860688
unambiguous semidirect product	C₃⋊(C₂×#16860688)

Splittings

Fitting, socle, derived	C₃×C₃₁×C₄₃ ⋊ C₂×C₃
Hall	C₃×#16860688 ⋊ C₂
Hall	C₃₁×C₄₃ ⋊ C₃×D₃
Sylow	C₄₃ ⋊ D₃×C₃₁⋊C₃
Sylow	C₃₁ ⋊ D₃×C₄₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₄₃	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₄₃
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 3999

A minimal faithful permutation representation — 2 generators on 77 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,30)(18,26,31)(21,29,28)(23,32,25)(27,36,38)(33,39,37)(34,40,35)(41,43,42)(45,46,48)(47,50,55)(49,53,52)(51,57,64)(54,60,62)(56,58,59)(61,67,71)(63,68,69)(65,72,66)(70,73,74)(76,77);(1,2,4,8,15,17,3,6,11,18,27,26,7,13,21,30,38,36,14,23,33,40,22,31,24,34,41,43,32,12,19,28,37,42,39,20,5,9,16,25,35,29,10)(44,45,47,51,58,48,52,59,66,72,55,62,69,57,65,64,71,74,67,50,56,63,70,73,60,46,49,54,61,68,53)(75,76,77)

Conjugacy classes & character table

1341 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23994, 53);

D3×#16860688 #37562045