Finite Group Databasebeta

D13×#3223 #16734294

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productD13×#3223

Splittings

FittingC13×#3223 ⋊ C2
SylowC13 ⋊ C2×#3223

Subgroups

subgroupG/H
centerC22C22×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3223C2
socleC22×C13C23×D4
prime radicalC2×#41×D13C22
hypercenter#3223D13
hypocenterC13C2×#3223
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #3223

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1040943);