Finite Group Databasebeta

C2×Q16×Dic86 #25977046

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

Aliases

direct productC2×Q16×Dic86

Splittings

SylowC43 ⋊ C2×Q8×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×Q16×C43C2
socle, prime radicalC23×C43C22×D4
hypercenterC2×C4×Q16D43
hypocenterC43C2×Q8×Q16
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

1830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1246 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1050017);