Finite Group Databasebeta

Q16×#10621902 #25978071

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

Aliases

direct productQ16×#10621902

Splittings

FittingQ8×Q16×C43 ⋊ C2
SylowC43 ⋊ Q16×#41

Subgroups

subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingQ8×Q16×C43C2
socleC22×C43C23×D4
prime radicalC2×#10621902D4
hypercenterQ8×Q16D43
hypocenterC43Q16×#41
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q8×Q16

1826 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

805 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1051042);