Finite Group Databasebeta

C2×#19135043 #25098356

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135043

Splittings

FittingC22×#117×C43 ⋊ C2
SylowC43 ⋊ C2×#1897

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#117×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC22×#117D43
hypocenterC43C2×#1897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×#117

1954 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171327);