Finite Group Databasebeta

← Prev (#72259333) Next (#72259335) →

D₄×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃ #72259334

order	7776
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

D₄×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃

Splittings

Fitting	D₄×#6891 ⋊ C₂²
Sylow	#6891 ⋊ C₂²×D₄

Subgroups

	subgroup	G/H
center	C₂	C₂²×(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃
commutator, cosocle	C₂×C₃²⋊C₉	C₂⁴×C₃
Frattini, socle	C₂×C₃²	C₂²×C₃×D₃²
Fitting	D₄×#6891	C₂²
hypercenter	D₄	(((C₃⋊D₃)⋊C₉)⋊C₂)⋊C₃
hypocenter	C₃²⋊C₉	C₂²×C₃×D₄
LCS	G ▷ C₂×C₃²⋊C₉ ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂ ◁ D₄

3540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 72

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

D₄×#72210336

GAP

Past the SmallGroups library coverage — no SmallGroups id.