Finite Group Databasebeta

C2×#19132517 #25005595

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132517

Splittings

SylowC43 ⋊ C2×#1313

Subgroups

subgroupG/H
centerC22×C4C4×Dic43
commutatorC4×C43C2×C4×C8
FrattiniC4×C8C22×D43
FittingC2×C43×#346C2
socle, prime radicalC23×C43#97
cosocleC4×C8×C43C23
hypercenterC2×#346D43
hypocenterC43C2×#1313
LCSG ▷ C4×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#346

302 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 78566);