Finite Group Databasebeta

C2×#19137413 #25255767

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#19137413

Splittings

FittingC2×C43×#386 ⋊ C2
SylowC43 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#386C2
socleC24×C43C24
prime radicalC23×D4×D43C2
cosocleC23×C43C25
hypercenterC2×#386D43
hypocenterC43C2×D4×C22⋊C4
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#386

8774 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328738);