Finite Group Databasebeta

C4×#16812760 #28378784

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16812760

Splittings

SylowC109 ⋊ C4×#101

Subgroups

subgroupG/H
centerC2×C4C22⋊#89137
commutatorC22×C109C2×C42
FrattiniC23C22×#89137
FittingC2×C42×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC23×C109C22×C4
cosocleC22×Dic109C23
hypercenterC2×C42#89137
hypocenterC109C4×#101
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

296 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 6976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20262);