Finite Group Databasebeta

C2×#13123668 #16727016

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13123668

Splittings

FittingC2×C13×#518 ⋊ C2
SylowC13 ⋊ C2×#2946

Subgroups

subgroupG/H
centerC23C22×C22⋊D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC2×C13×#518C2
socleC23×C13C22×D4
prime radicalC22×#88186C2
cosocleC2×C4×C13C25
hypercenterC2×#518D13
hypocenterC13C2×#2946
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

2946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033665);