Finite Group Databasebeta

← Prev (#25960599) Next (#25960601) →

C22×C4×D344 #25960600

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×C4×D344

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C22×C4×D8

Subgroups

subgroupG/H
centerC23×C4D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×C4×C8×C43C2
socleC24×C43C2×D4
prime radicalC23×D344C2
cosocleC2×C4×C43C25
hypercenterC22×C4×C8D43
hypocenterC43C22×C4×D8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

3694 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, 1033571);