Finite Group Databasebeta

Q8×#13063331 #25961008

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productQ8×#13063331

Splittings

FittingC2×C8×Q8×C43 ⋊ C2
SylowC43 ⋊ Q8×#131

Subgroups

subgroupG/H
centerC2×C8C23×D43
commutator, socleC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C8×Q8×C43C2
prime radicalC2×#10621898C23
cosocleC2×C4×C43C25
hypercenterC2×C8×Q8D43
hypocenterC43Q8×#131
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C2×C8×Q8

1882 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033979);