Finite Group Databasebeta

C2×#19143056 #25960067

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

Aliases

direct productC2×#19143056

Splittings

SylowC43 ⋊ C2×#2883

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
Fitting, prime radicalC22×H(5,𝔽2)×C43C2
socleC22×C43C22×C22⋊C4
cosocleC23×C43C25
hypercenterC22×H(5,𝔽2)D43
hypocenterC43C2×#2883
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×D4 ◁ C22×H(5,𝔽2)

5338 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, 1033038);