Finite Group Databasebeta

C2×C4×C22⋊#89137 #28379460

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×C22⋊#89137

Splittings

FittingC23×C4×C109 ⋊ C4
SylowC109 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×#89137
commutatorC2×C109C22×C42
FrattiniC22C23×#89137
FittingC23×C4×C109C4
socleC23×C109C22×C4
prime radicalC24×D109C22
cosocleC22×D109C24
hypercenterC23×C4#89137
hypocenterC109C2×C4×C22⋊C4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C23×C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20938);