Finite Group Databasebeta

Q8×#4047 #12963711

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#4047

Splittings

FittingC2×C5×C8×Q8 ⋊ C2
SylowC5 ⋊ Q8×#131

Subgroups

subgroupG/H
centerC2×C8C23×D5
commutator, socleC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC2×C5×C8×Q8C2
prime radicalC2×#709C23
cosocleC2×C4×C5C25
hypercenterC2×C8×Q8D5
hypocenterC5Q8×#131
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C2×C8×Q8

1882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1033979);