Finite Group Databasebeta

C4×#16812681 #28365552

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#16812681

Splittings

FittingC4×C22⋊C4×C109 ⋊ C2
SylowC109 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC22×C109C23×C4
FrattiniC23C23×D109
FittingC4×C22⋊C4×C109C2
socle, cosocleC23×C109C24
prime radicalC22×C22⋊D109C22
hypercenterC4×C22⋊C4D109
hypocenterC109C4×#123
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 7030);