Finite Group Databasebeta

Q8×#13063260 #25115487

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productQ8×#13063260

Splittings

SylowC43 ⋊ Q8×#108

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingQ8×M16×C43C2
socleC22×C43C22×C4⋊C4
prime radicalC23×C43C22×Q8
cosocleC22×C4×C43C24
hypercenterQ8×M16D43
hypocenterC43Q8×#108
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ Q8×M16

658 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, 188458);