Finite Group Databasebeta

C2×#19133432 #25066110

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

Aliases

direct productC2×#19133432

Splittings

SylowC43 ⋊ C2×#1582

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C4×D4
prime radicalC22×D4×C43C2×C4
cosocleC42×C43C24
hypercenterC2×C4×SD16D43
hypocenterC43C2×#1582
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

762 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, 139081);