Finite Group Databasebeta

C23×#88064 #16726403

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#88064

Splittings

SylowC13 ⋊ C23×#101

Subgroups

subgroupG/H
centerC24#6103
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC23×C13×M16C2
socleC24×C13C22⋊C4
prime radicalC25×C13C2×C4
cosocleC2×C4×C13C25
hypercenterC23×M16D13
hypocenterC13C23×#101
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×M16

4990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1033052);