Finite Group Databasebeta

C2×#13123427 #16726582

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#13123427

Splittings

FittingC22×C13×#106 ⋊ C2
SylowC13 ⋊ C2×#2912

Subgroups

subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#106C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
cosocleC2×C4×C13C25
hypercenterC22×#106D13
hypocenterC13C2×#2912
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

2766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033231);