Finite Group Databasebeta

C23×#88046 #16726379

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#88046

Splittings

FittingC23×C13×C22⋊C4 ⋊ C2
SylowC13 ⋊ C23×#99

Subgroups

subgroupG/H
centerC24#6103
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC23×C13×C22⋊C4C2
socleC24×C13C22⋊C4
prime radicalC24×C22⋊D13C2
cosocleC23×C13C25
hypercenterC23×C22⋊C4D13
hypocenterC13C23×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C26 ◁ C23×C22⋊C4

7902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033028);