Finite Group Databasebeta

← Prev (#64320) Next (#64322) →

C₂²×D₃×Dic₃ #64321

order	288
isoclinism	isoclinic class of D₃²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₃×Dic₃

Splittings

C₃² ⋊ C₂³×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂³	D₃²
commutator, hypocenter	C₃²	C₂³×C₄
Frattini	C₂	C₂²×D₃²
Fitting, socle	C₂³×C₃²	C₂²
prime radical	C₂³×C₃×D₃	C₂
cosocle	C₂×C₃²	C₂⁴
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂³

499 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 4 generators on 14 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₃⋊#95, #10591362, #10591363, …
maximal normal subgroup of	D₃×C₃⋊#95, #10591362, #10591363, …
maximal quotient of	C₂²×D₃×C₃⋊C₈, C₂×D₃×#208, C₂×#63814, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 969);