Finite Group Databasebeta

C2×#13116551 #16015805

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13116551

Splittings

FittingC2×C13×#427 ⋊ C2
SylowC13 ⋊ C2×#2140

Subgroups

subgroupG/H
centerC23C2×#6104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC2×C13×#427C2
socleC23×C13C2×D8
prime radicalC23×D104C2
cosocleC2×C8×C13C24
hypercenterC2×#427D13
hypocenterC13C2×#2140
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

1406 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322454);