Finite Group Databasebeta

C2×#19136264 #25249382

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19136264

Splittings

SylowC43 ⋊ C2×#2127

Subgroups

subgroupG/H
centerC22C2×#13063240
commutatorC2×C4×C43C23×C4
FrattiniC2×D4C23×D43
Fitting, prime radicalC2×C43×#535C2
socleC22×C43C2×#99
cosocleC2×D4×C43C24
hypercenterC2×#535D43
hypocenterC43C2×#2127
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C2×#535

1510 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

970 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322353);