Finite Group Databasebeta

C2×#13130018 #16791681

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#13130018
unambiguous semidirect productD13⋊#1438

Splittings

FittingC23×D4×C13 ⋊ C4
SylowC13 ⋊ C2×#1438

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC23×D4×C13C4
socleC24×C13C22×C4
prime radicalC23×D4×D13C2
cosocleC23×D13C24
hypercenterC23×D4#261
hypocenterC13C2×#1438
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×D4

8190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1098330);