Finite Group Databasebeta

C2×#13112995 #15783201

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

Aliases

direct productC2×#13112995

Splittings

SylowC13 ⋊ C2×#1407

Subgroups

subgroupG/H
centerC22#11718066
commutatorC42×C13C22×C4
Frattini#124C22×D13
FittingC2×C13×#354C2
socleC22×C13#353
prime radicalC22×D4×C13D4
cosocleC13×#124C23
hypercenterC2×#354D13
hypocenterC13C2×#1407
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ C2×#354

416 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 75 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) = 832

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 89850);