Finite Group Databasebeta

C2×#13131276 #16807457

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#13131276
unambiguous semidirect productD13⋊#2276

Splittings

FittingC2×C4×Q8×C13 ⋊ C4
SylowC13 ⋊ C2×#2276

Subgroups

subgroupG/H
centerC23C23×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC2×C4×Q8×C13C4
socleC23×C13C23×C4
prime radicalC23×D13C24
cosocleC22×D13C25
hypercenterC2×C4×Q8#261
hypocenterC13C2×#2276
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8

3654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114106);