C₆₇×C₃⋊D₃₃ #27210725

order	13266
isoclinism	isoclinic class of C₃⋊D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₇ · Schur multiplier (H₂) = C₃

Aliases

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

Splittings

Fitting, socle, Hall	C₃²×C₁₁×C₆₇ ⋊ C₂
derived, Hall	C₃²×C₁₁ ⋊ C₂×C₆₇
Hall	C₁₁×C₆₇ ⋊ C₃⋊D₃
Hall	C₃²×C₆₇ ⋊ D₁₁
Sylow	C₁₁ ⋊ C₃⋊D₃×C₆₇
Sylow	C₃² ⋊ D₁₁×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₆₇	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂×C₆₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₆₇	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₆₇

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 84
transitive degree	μ_t(G) = 6633

A minimal faithful permutation representation — 3 generators on 84 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(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);(1,2,4,6,8,10,11,9,7,5,3)(15,16,17);(12,13,14)

Conjugacy classes & character table

3417 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₃₃×C₆₇, D₂₀₁⋊D₃₃, D₆₇×C₃⋊D₃₃, …
maximal normal subgroup of	D₃×D₃₃×C₆₇, D₂₀₁⋊D₃₃, D₆₇×C₃⋊D₃₃, …
maximal quotient of	C₆₇×C₃⋊Dic₃₃, C₂×C₆₇×C₃⋊D₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13266, 39);

C67×C3⋊D33 #27210725