D₃₃×C₆₇⋊C₃ #27210722

order	13266
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃₃×C₆₇⋊C₃
unambiguous semidirect product	C₃⋊(D₁₁×C₆₇⋊C₃)
unambiguous semidirect product	C₁₁⋊(D₃×C₆₇⋊C₃)
unambiguous semidirect product	(D₃₃×C₆₇)⋊C₃

Splittings

Fitting, socle, derived	C₃×C₁₁×C₆₇ ⋊ C₂×C₃
Hall	C₃×C₁₁×C₆₇⋊C₃ ⋊ C₂
Hall	C₁₁×C₆₇ ⋊ C₃×D₃
Hall	C₃×C₆₇⋊C₃ ⋊ D₁₁
Sylow	C₆₇ ⋊ C₃×D₃₃
Sylow	C₁₁ ⋊ D₃×C₆₇⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₆₇	C₂×C₃
LCS	G ▷ C₃×C₁₁×C₆₇
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 2211

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃₃×D₆₇⋊C₃, D₃₃⋊(D₆₇⋊C₃), D₃×D₁₁×C₆₇⋊C₃, …
maximal normal subgroup of	D₃₃×D₆₇⋊C₃, D₃₃⋊(D₆₇⋊C₃), D₃×D₁₁×C₆₇⋊C₃, …
maximal quotient of	Dic₃₃×C₆₇⋊C₃, C₂×D₃₃×C₆₇⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 36);

D33×C67⋊C3 #27210722