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C₁₆×C₃⋊D₃ #63624

order	288
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₁₆×C₃⋊D₃

Splittings

Fitting	C₃²×C₁₆ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₁₆	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₁₆
Frattini	C₈	C₂×C₃⋊D₃
Fitting	C₃²×C₁₆	C₂
socle	C₂×C₃²	C₂×C₈
prime radical	C₂×C₃⋊D₃	C₈
cosocle	C₃²×C₈	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₆

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 22 points:

(18,19)(21,22);(1,2,3,6,4,7,9,12,5,8,10,13,11,14,15,16)(20,21,22);(17,18,19)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10589067, #10589069, C₃⋊D₃×C₃₂, …
maximal normal subgroup of	#10589067, #10589069, C₃⋊D₃×C₃₂, …
maximal quotient of	C₃⋊D₃×C₃₂, #10589313, C₁₆×C₃⋊Dic₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 272);