Finite Group Databasebeta

Q8×#13063246 #25113186

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ8×#13063246

Splittings

SylowC43 ⋊ Q8×#102

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×D4×Q8×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC2×D4×Q8D43
hypocenterC43Q8×#102
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

1314 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 186157);