Finite Group Databasebeta

C23×#88052 #16769380

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC23×#88052

Splittings

SylowC13 ⋊ C23×M32

Subgroups

subgroupG/H
centerC23×C8C2×D13
commutatorC2×C13C24×C8
FrattiniC8C24×D13
FittingC24×C8×C13C2
socleC24×C13C2×C8
prime radicalC25×C13C8
cosocleC8×C13C25
hypercenterC24×C8D13
hypocenterC13C23×M32
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C8 ◁ C24×C8

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076029);