Finite Group Databasebeta

C2×#13118372 #16030385

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13118372

Splittings

FittingC23×C13×C22⋊C4 ⋊ C2
SylowC13 ⋊ C2×#2424

Subgroups

subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC23×C13×C22⋊C4C2
socleC24×C13C24
hypercenterC23×C22⋊C4D13
hypocenterC13C2×#2424
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C22⋊C4

5898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 337034);