Finite Group Databasebeta

← Prev (#88777) Next (#88779) →

C₃×Dic₃² #88778

order	432
isoclinism	isoclinic class of D₃²
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₄

Aliases

C₃×Dic₃²

Splittings

derived	C₃² ⋊ C₃×C₄²
Sylow	C₃³ ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₃²
commutator, hypocenter	C₃²	C₃×C₄²
Frattini	C₂²	C₃×D₃²
Fitting, socle, prime radical	C₂²×C₃³	C₂²
cosocle	C₂²×C₃²	C₂²×C₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²×C₃

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 17 points:

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

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#63741, #11722776, D₃×Dic₃², …
maximal normal subgroup of	C₃×#63741, #11722776, D₃×Dic₃², …
maximal quotient of	C₃×Dic₃×C₃⋊C₈, C₃×#63553, C₃×#63554, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 425);