Finite Group Databasebeta

C2×#13129899 #16789110

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13129899

Splittings

FittingC2×C13×#108 ⋊ C4
SylowC13 ⋊ C2×#1382

Subgroups

subgroupG/H
centerC2×C4#88115
commutatorC8×C13C2×C42
FrattiniC2×C8C22×#261
FittingC2×C13×#108C4
socleC22×C13#340
prime radicalC23×D13SD16
cosocleC2×C8×D13C23
hypercenterC2×#108#261
hypocenterC13C2×#1382
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

590 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, 1095759);