Finite Group Databasebeta

Q8×M16×D43 #25960980

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

Aliases

direct productQ8×M16×D43

Splittings

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

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingQ8×M16×C43C2
prime radicalC23×D43C22×C4
cosocleC2×C4×C43C25
hypercenterQ8×M16D43
hypocenterC43C2×Q8×M16
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ Q8×M16

2154 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033951);