Finite Group Databasebeta

C2×#19132421 #24984540

order11008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132421

Splittings

SylowC43 ⋊ C2×#1272

Subgroups

subgroupG/H
centerC24C22⋊Dic43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×#391C2
socle, prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#391D43
hypocenterC43C2×#1272
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#391

778 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 57511);