Finite Group Databasebeta

C2×#19144000 #25963335

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19144000

Splittings

FittingC2×C43×#536 ⋊ C2
SylowC43 ⋊ C2×#3028

Subgroups

subgroupG/H
centerC22C2×#13063293
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#536C2
socleC22×C43C2×#120
prime radicalC2×#14583735C2
hypercenterC2×#536D43
hypocenterC43C2×#3028
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

4790 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036306);