Finite Group Databasebeta

C2×#19143078 #25960097

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19143078

Splittings

SylowC43 ⋊ C2×#2889

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
Fitting, prime radicalC22×2−1+4×C43C2
socleC22×C43C22×C22⋊C4
cosocleC2×C4×C43C25
hypercenterC22×2−1+4D43
hypocenterC43C2×#2889
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×2−1+4

4770 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033068);