Finite Group Databasebeta

C2×C8×D344 #25065955

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C8×D344

Splittings

FittingC2×C82×C43 ⋊ C2
SylowC43 ⋊ C2×C8×D8

Subgroups

subgroupG/H
centerC22×C8D172
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC2×C82×C43C2
socleC23×C43C4×D4
prime radicalC22×D344C4
cosocleC42×C43C24
hypercenterC2×C82D43
hypocenterC43C2×C8×D8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C82

910 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 138926);