Finite Group Databasebeta

C2×#19143231 #25960326

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#19143231

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C2×#2921

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×M16×C43C2
socleC23×C43C23×C4
prime radicalC24×D43C2×C4
cosocleC2×C4×C43C25
hypercenterC2×C4×M16D43
hypocenterC43C2×#2921
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

2198 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, 1033297);