Finite Group Databasebeta

C2×#19133254 #25064898

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19133254

Splittings

FittingC2×C43×#331 ⋊ C2
SylowC43 ⋊ C2×#1543

Subgroups

subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#331C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583447C2
cosocleC42×C43C24
hypercenterC2×#331D43
hypocenterC43C2×#1543
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

1274 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 137869);