Finite Group Databasebeta

C2×#13112943 #15777835

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13112943

Splittings

SylowC13 ⋊ C2×#1386

Subgroups

subgroupG/H
centerC23#88049
commutatorC8×C13C2×C42
FrattiniC22×C8C22×D13
FittingC22×C13×#106C2
socleC23×C13#102
prime radicalC24×C13D8
cosocleC22×C8×C13C23
hypercenterC22×#106D13
hypocenterC13C2×#1386
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#106

630 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, 84484);