Finite Group Databasebeta

C2×#19132641 #25007833

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132641

Splittings

SylowC43 ⋊ C2×#1361

Subgroups

subgroupG/H
centerC23#13063246
commutatorC2×C8×C43C22×C4
FrattiniC4×C8C22×D43
Fitting, prime radicalC2×C43×#493C2
socleC23×C43#102
cosocleC4×C8×C43C23
hypercenterC2×#493D43
hypocenterC43C2×#1361
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#493

518 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 80804);