Finite Group Databasebeta

C2×#19149219 #26003997

order11008
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#19149219

Splittings

FittingC22×#126×C43 ⋊ C2
SylowC43 ⋊ C2×#3564

Subgroups

subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC22×#126×C43C2
socleC23×C43C25
prime radicalC2×#14583487C2
hypercenterC22×#126D43
hypocenterC43C2×#3564
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#126

6598 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076968);