Finite Group Databasebeta

C2×#19136492 #25250037

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

Aliases

direct productC2×#19136492

Splittings

FittingC2×C43×#365 ⋊ C2
SylowC43 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC22#14583010
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#365C2
socleC22×C43#442
prime radicalC2×#14583337C2
cosocleC2×C8×C43C24
hypercenterC2×#365D43
hypocenterC43C2×AGL(1,ℤ/16)
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

710 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

718 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323008);