C₂₃×C₃⋊D₃₃ #17986927

order	4554
isoclinism	isoclinic class of C₃⋊D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂₃×C₃⋊D₃₃
unambiguous semidirect product	C₃⋊(C₂₃×D₃₃)
unambiguous semidirect product	C₁₁⋊(C₃⋊D₃×C₂₃)

Splittings

Fitting, socle, Hall	C₃²×C₁₁×C₂₃ ⋊ C₂
derived, Hall	C₃²×C₁₁ ⋊ C₂×C₂₃
Hall	C₁₁×C₂₃ ⋊ C₃⋊D₃
Hall	C₃²×C₂₃ ⋊ D₁₁
Sylow	C₁₁ ⋊ C₃⋊D₃×C₂₃
Sylow	C₃² ⋊ D₁₁×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₂₃	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 2277

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,26)(27,28)(29,30)(31,32)(33,34)(36,37)(39,40);(24,25,27,29,31,33,34,32,30,28,26)(38,39,40);(35,36,37)

Conjugacy classes & character table

1173 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×C₃⋊(C₃⋊AGL(1,𝔽₁₁)), C₅×C₂₃×C₃⋊D₃₃, C₂₃×C₃⋊D₁₆₅, …
maximal normal subgroup of	C₂₃×C₃⋊(C₃⋊AGL(1,𝔽₁₁)), C₅×C₂₃×C₃⋊D₃₃, C₇×C₂₃×C₃⋊D₃₃
maximal quotient of	C₅×C₂₃×C₃⋊D₃₃, C₂₃×C₃⋊D₁₆₅, C₇×C₂₃×C₃⋊D₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 29);

C23×C3⋊D33 #17986927