Finite Group Databasebeta

C22×Dic688 #25254720

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic688

Splittings

SylowC43 ⋊ C22×Q64

Subgroups

subgroupG/H
centerC23D688
commutator, cosocleC16×C43C24
FrattiniC16C23×D43
FittingC22×C32×C43C2
socle, prime radicalC23×C43D16
hypercenterC22×C32D43
hypocenterC43C22×Q64
LCSG ▷ C16×C43 ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×C32

462 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327691);