Finite Group Databasebeta

C2×#13113003 #15783244

order3328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#13113003

Splittings

SylowC13 ⋊ C2×#1410

Subgroups

subgroupG/H
centerC22#11718137
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC2×C13×#492C2
socleC22×C13#353
prime radicalC2×C13×#127C4
cosocleC13×C4⋊Q8C23
hypercenterC2×#492D13
hypocenterC13C2×#1410
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ C2×#492

450 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

298 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 89893);