Finite Group Databasebeta

C2×#19135265 #25099179

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

Aliases

direct productC2×#19135265

Splittings

FittingC2×C43×#339 ⋊ C2
SylowC43 ⋊ C2×#1932

Subgroups

subgroupG/H
centerC2×C4#13063300
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#339C2
socleC22×C43#388
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#339D43
hypocenterC43C2×#1932
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

1046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 172150);