Finite Group Databasebeta

C4×#11718242 #16780682

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#11718242

Splittings

SylowC13 ⋊ C4×#330

Subgroups

subgroupG/H
centerC22×C4C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13C4×#330
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

532 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 3328

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087331);