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C₄×D₃₃ #63156

order	264
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₄×D₃₃

Splittings

Fitting	C₃×C₄×C₁₁ ⋊ C₂
derived, Hall	C₃×C₁₁ ⋊ C₂×C₄
Sylow	C₁₁ ⋊ C₄×D₃
Sylow	C₃ ⋊ C₄×D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄	D₃₃
commutator, hypocenter	C₃×C₁₁	C₂×C₄
Frattini	C₂	C₂×D₃₃
Fitting	C₃×C₄×C₁₁	C₂
socle, cosocle	C₂×C₃×C₁₁	C₂²
prime radical	C₂×D₃₃	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₄

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,14);(1,2,4,6,8,10,11,9,7,5,3)(12,13,14)(15,16,17,18)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃₃⋊C₈, #10587140, C₈×D₃₃, …
maximal normal subgroup of	D₃₃⋊C₈, #10587140, C₈×D₃₃, …
maximal quotient of	C₈×D₃₃, #10587194, C₄×Dic₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 24);