Finite Group Databasebeta

C2×C4×D688 #25249859

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×C4×D688

Splittings

FittingC2×C4×C16×C43 ⋊ C2
SylowC43 ⋊ C2×C4×D16

Subgroups

subgroupG/H
centerC22×C4D344
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C4×C16×C43C2
socleC23×C43C2×D8
prime radicalC22×D688C2
cosocleC2×C8×C43C24
hypercenterC2×C4×C16D43
hypocenterC43C2×C4×D16
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

806 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322830);