Finite Group Databasebeta

C2×#13115298 #15864737

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#13115298

Splittings

FittingC2×C13×#343 ⋊ C2
SylowC13 ⋊ C2×#1900

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#343C2
socleC23×C13C2×C22⋊C4
prime radicalC22×#88149C2
cosocleC22×C4×C13C24
hypercenterC2×#343D13
hypocenterC13C2×#1900
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

2198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 171386);