Finite Group Databasebeta

C2×#19133251 #25064894

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19133251

Splittings

FittingC2×C43×#332 ⋊ C2
SylowC43 ⋊ C2×#1542

Subgroups

subgroupG/H
centerC23C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×#332C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC42×C43C24
hypercenterC2×#332D43
hypocenterC43C2×#1542
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

1050 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 137865);