Finite Group Databasebeta

C2×#13123444 #16726614

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

Aliases

direct productC2×#13123444

Splittings

FittingC22×C13×#108 ⋊ C2
SylowC13 ⋊ C2×#2916

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#108C2
socleC22×C13C22×C4⋊C4
prime radicalC22×#6127C22
cosocleC2×C4×C13C25
hypercenterC22×#108D13
hypocenterC13C2×#2916
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#108

2586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1033263);