Finite Group Databasebeta

Q8×#13063241 #25113156

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#13063241

Splittings

FittingQ8×M16×C43 ⋊ C2
SylowC43 ⋊ Q8×#100

Subgroups

subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingQ8×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterQ8×M16D43
hypocenterC43Q8×#100
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

1198 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 186127);