Finite Group Databasebeta

C2×#19133435 #25066098

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

Aliases

direct productC2×#19133435

Splittings

FittingC2×C43×Q8⋊C8 ⋊ C2
SylowC43 ⋊ C2×#1583

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×Q8⋊C8C2
socleC23×C43C4×D4
prime radicalC22×D172C2×C4
cosocleC42×C43C24
hypercenterC2×Q8⋊C8D43
hypocenterC43C2×#1583
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

750 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, 139069);