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D₃₂×D₈₉ #26022548

order	11392
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₃₂×D₈₉

Splittings

Fitting	D₃₂×C₈₉ ⋊ C₂
Sylow	C₈₉ ⋊ C₂×D₃₂

Subgroups

	subgroup	G/H
center	C₂	D₁₆×D₈₉
commutator, cosocle	C₁₆×C₈₉	C₂³
Frattini	C₁₆	C₂²×D₈₉
Fitting	D₃₂×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₁₆
hypercenter	D₃₂	D₈₉
hypocenter	C₈₉	C₂×D₃₂
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₆₄×D₈₉, SD₁₂₈×D₈₉, #36475484, …
maximal normal subgroup of	D₆₄×D₈₉, SD₁₂₈×D₈₉, #36475484, …
maximal quotient of	#1415×D₈₉, #1423×D₈₉, #36474999, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 6806);