Finite Group Databasebeta

Q8×#13063345 #25977060

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

Aliases

direct productQ8×#13063345

Splittings

FittingQ8×#41×C43 ⋊ C2
SylowC43 ⋊ Q8×#135

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingQ8×#41×C43C2
socleC22×C43C23×D4
prime radicalC2×#13063345C22
hypercenterQ8×#41D43
hypocenterC43Q8×#135
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ Q8×#41

1786 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, 1050031);