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D₁₆×D₈₉ #19152017

order	5696
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₁₆×D₈₉

Splittings

Fitting	D₁₆×C₈₉ ⋊ C₂
Sylow	C₈₉ ⋊ C₂×D₁₆

Subgroups

	subgroup	G/H
center	C₂	D₈×D₈₉
commutator	C₈×C₈₉	C₂³
Frattini	C₈	C₂²×D₈₉
Fitting	D₁₆×C₈₉	C₂
socle	C₂×C₈₉	C₂×D₈
hypercenter	D₁₆	D₈₉
hypocenter	C₈₉	C₂×D₁₆
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃₂×D₈₉, SD₆₄×D₈₉, #26022563, …
maximal normal subgroup of	D₃₂×D₈₉, SD₆₄×D₈₉, #26022563, …
maximal quotient of	#357×D₈₉, #366×D₈₉, #26022096, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5696, 968);