Finite Group Databasebeta

C2×#19135075 #25098462

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

Aliases

direct productC2×#19135075

Splittings

FittingC2×C43×#568 ⋊ C2
SylowC43 ⋊ C2×#1903

Subgroups

subgroupG/H
centerC22#14582778
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#568C2
socleC22×C43#386
prime radicalC22×#13063350C2
cosocleC22×C4×C43C24
hypercenterC2×#568D43
hypocenterC43C2×#1903
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#568

1782 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1486 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 171433);