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C₂²×C₃×C₃⋊Dic₃ #89071

order	432
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂²×C₃×C₃⋊Dic₃

Splittings

derived	C₃² ⋊ C₂²×C₃×C₄
Sylow	C₃³ ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂³×C₃	C₃⋊D₃
commutator, hypocenter	C₃²	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×C₃⋊D₃
Fitting, socle, prime radical	C₂³×C₃³	C₂
cosocle	C₂×C₃²	C₂³×C₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂³×C₃

452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#63579, #11722061, #11722082, …
maximal normal subgroup of	C₃×#63579, #11722061, #11722082, …
maximal quotient of	C₂²×C₃×C₃⋊(C₃⋊C₈), C₂×C₃×#3748, C₂×C₃×C₄×C₃⋊Dic₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 718);