Finite Group Databasebeta

C2×#13114087 #15838722

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13114087

Splittings

FittingC2×C13×Q8⋊C8 ⋊ C2
SylowC13 ⋊ C2×#1649

Subgroups

subgroupG/H
centerC23#88136
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×Q8⋊C8C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×Q8⋊C8D13
hypocenterC13C2×#1649
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

1206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 145371);