Finite Group Databasebeta

#104×C22⋊D13 #15878589

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#104×C22⋊D13

Splittings

FittingC22×C13×#104 ⋊ C2
SylowC13 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×#104C2
socleC22×C13C22×C22⋊C4
prime radical#41×C22⋊D13C2
cosocleC22×C4×C13C24
hypercenterC22×#104D13
hypocenterC13D4×#104
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 185238);