Finite Group Databasebeta

C23×#88074 #16726380

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

Aliases

direct productC23×#88074

Splittings

SylowC13 ⋊ C23×#99

Subgroups

subgroupG/H
centerC24C22⋊Dic13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
Fitting, prime radicalC24×D4×C13C2
socleC24×C13C22⋊C4
cosocleC23×C13C25
hypercenterC24×D4D13
hypocenterC13C23×#99
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C26 ◁ C24×D4

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, 1033029);