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D₈×D₉₈₃ #44537972

order	31456
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₈×D₉₈₃

Splittings

Fitting	D₈×C₉₈₃ ⋊ C₂
Sylow	C₉₈₃ ⋊ C₂×D₈

Subgroups

	subgroup	G/H
center	C₂	D₄×D₉₈₃
commutator, cosocle	C₄×C₉₈₃	C₂³
Frattini	C₄	C₂²×D₉₈₃
Fitting	D₈×C₉₈₃	C₂
socle	C₂×C₉₈₃	C₂×D₄
hypercenter	D₈	D₉₈₃
hypocenter	C₉₈₃	C₂×D₈
LCS	G ▷ C₄×C₉₈₃ ▷ C₂×C₉₈₃ ▷ C₉₈₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7864

Conjugacy classes & character table

3451 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31456, 155);