Finite Group Databasebeta

C2×#13131003 #16799235

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#13131003
unambiguous semidirect productD13⋊#1982

Splittings

FittingC2×C13×#127 ⋊ C4
SylowC13 ⋊ C2×#1982

Subgroups

subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#127C4
socleC23×C13C2×C22⋊C4
prime radicalC2×D13×#127C2
cosocleC2×C4×D13C24
hypercenterC2×#127#261
hypocenterC13C2×#1982
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

2374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1105884);