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Q₃₂×D₈₃ #19128127

order	5312
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₃₂×D₈₃

Splittings

Fitting	Q₃₂×C₈₃ ⋊ C₂
Sylow	C₈₃ ⋊ C₂×Q₃₂

Subgroups

	subgroup	G/H
center	C₂	D₈×D₈₃
commutator	C₈×C₈₃	C₂³
Frattini	C₈	C₂²×D₈₃
Fitting	Q₃₂×C₈₃	C₂
socle	C₂×C₈₃	C₂×D₈
hypercenter	Q₃₂	D₈₃
hypocenter	C₈₃	C₂×Q₃₂
LCS	G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

82 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

473 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₆₄×D₈₃, Q₆₄×D₈₃, #24909779, …
maximal normal subgroup of	SD₆₄×D₈₃, Q₆₄×D₈₃, #24909779, …
maximal quotient of	#358×D₈₃, #366×D₈₃, #24909319, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5312, 975);