Finite Group Databasebeta

D13×#2100 #15892825

order3328
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productD13×#2100

Splittings

FittingC13×#2100 ⋊ C2
SylowC13 ⋊ C2×#2100

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2100C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenter#2100D13
hypocenterC13C2×#2100
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 199474);