Finite Group Databasebeta

C2×#19133039 #25063015

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

Aliases

direct productC2×#19133039

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C2×#1490

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C4×M16×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D172C4
cosocleC42×C43C24
hypercenterC2×C4×M16D43
hypocenterC43C2×#1490
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

1734 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135986);