Finite Group Databasebeta

D13×#1573 #15831995

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productD13×#1573

Splittings

FittingC13×#1573 ⋊ C2
SylowC13 ⋊ C2×#1573

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1573C2
socleC22×C13C22×C4⋊C4
prime radicalC23×D13C4⋊C4
cosocleC42×C13C24
hypercenter#1573D13
hypocenterC13C2×#1573
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 138644);