Finite Group Databasebeta

C2×#19134398 #25094298

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#19134398

Splittings

SylowC43 ⋊ C2×#1757

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC22×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C43×#413C2
socleC22×C43C4×C22⋊C4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#413D43
hypocenterC43C2×#1757
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

1474 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167269);