Finite Group Databasebeta

C2×M16×Dic86 #25960984

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

Aliases

direct productC2×M16×Dic86

Splittings

SylowC43 ⋊ C2×Q8×M16

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×M16×C43C2
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
cosocleC2×C4×C43C25
hypercenterC2×C4×M16D43
hypocenterC43C2×Q8×M16
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

2154 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033955);