Finite Group Databasebeta

Q8×#13063347 #25977066

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#13063347

Splittings

FittingC2×C8×Q8×C43 ⋊ C2
SylowC43 ⋊ Q8×#135

Subgroups

subgroupG/H
centerC2×C4C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C8×Q8×C43C2
socleC22×C43C23×D4
prime radicalC2×#13063347C22
hypercenterC2×C8×Q8D43
hypocenterC43Q8×#135
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ C2×C8×Q8

1786 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1050037);