Finite Group Databasebeta

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Q8×D5×C4⋊C4 #12258598

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×D5×C4⋊C4

Splittings

FittingC5×Q8×C4⋊C4 ⋊ C2
SylowC5 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D5
commutatorC22×C5C24×C4
FittingC5×Q8×C4⋊C4C2
socle, cosocleC23×C5C25
prime radicalC23×D5C24
hypercenterQ8×C4⋊C4D5
hypocenterC5C2×Q8×C4⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 328866);