Finite Group Databasebeta

C2×#13113288 #15829516

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

Aliases

direct productC2×#13113288

Splittings

FittingC22×C4×C8×C13 ⋊ C2
SylowC13 ⋊ C2×#1492

Subgroups

subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC22×C4×C8×C13C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#11719182C2
cosocleC42×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C2×#1492
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

1430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 136165);