Finite Group Databasebeta

C2×#19133047 #25063194

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19133047

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C2×#1492

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583449C2
cosocleC42×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C2×#1492
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

1430 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 136165);