Finite Group Databasebeta

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Q8×#3939 #12118137

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#3939

Splittings

SylowC5 ⋊ Q8×#107

Subgroups

subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×Q8×C4⋊C4C2
socle, prime radicalC23×C5C22×D4
cosocleC22×C4×C5C24
hypercenterQ8×C4⋊C4D5
hypocenterC5Q8×#107
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ Q8×C4⋊C4

838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 188405);