Finite Group Databasebeta

D13×#1778 #15861018

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productD13×#1778

Splittings

FittingC13×#1778 ⋊ C2
SylowC13 ⋊ C2×#1778

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1778C2
socleC22×C13C22×C4⋊C4
prime radicalC23×D13C2×Q8
cosocleC22×C4×C13C24
hypercenter#1778D13
hypocenterC13C2×#1778
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1778

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 167667);