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D₆₄×D₈₉ #36475469

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₆₄×D₈₉

Splittings

Fitting	C₈₉×D₆₄ ⋊ C₂
Sylow	C₈₉ ⋊ C₂×D₆₄

Subgroups

	subgroup	G/H
center	C₂	D₃₂×D₈₉
commutator, cosocle	C₃₂×C₈₉	C₂³
Frattini	C₃₂	C₂²×D₈₉
Fitting	C₈₉×D₆₄	C₂
socle	C₂×C₈₉	C₂×D₃₂
hypercenter	D₆₄	D₈₉
hypocenter	C₈₉	C₂×D₆₄
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5696

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 90609);