D₃×#16838389 #37523880

order	22914
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#16838389
unambiguous semidirect product	C₃⋊(C₂×#16838389)

Splittings

Fitting, socle, derived	C₃×C₁₉×C₆₇ ⋊ C₂×C₃
Hall	C₃×#16838389 ⋊ C₂
Hall	C₁₉×C₆₇ ⋊ C₃×D₃
Sylow	C₆₇ ⋊ D₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ D₃×C₆₇⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₆₇	C₂×C₃
LCS	G ▷ C₃×C₁₉×C₆₇
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 3819

A minimal faithful permutation representation — 2 generators on 89 points:

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

Conjugacy classes & character table

1281 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22914, 65);

D3×#16838389 #37523880