Finite Group Databasebeta

C22×D13×#100 #16726399

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×D13×#100

Splittings

FittingC22×C13×#100 ⋊ C2
SylowC13 ⋊ C23×#100

Subgroups

subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#100C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D4×D13C2
cosocleC2×C4×C13C25
hypercenterC22×#100D13
hypocenterC13C23×#100
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

7134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033048);