Finite Group Databasebeta

C2×#13131143 #16806954

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

Aliases

direct productC2×#13131143
unambiguous semidirect productD13⋊#2138

Splittings

FittingC2×C13×#135 ⋊ C4
SylowC13 ⋊ C2×#2138

Subgroups

subgroupG/H
centerC2×C4#88115
commutatorC8×C13C23×C4
FrattiniC8C23×#261
FittingC2×C13×#135C4
socleC22×C13C2×#102
prime radicalC2×D13×#135C2
cosocleC8×D13C24
hypercenterC2×#135#261
hypocenterC13C2×#2138
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113603);