Finite Group Databasebeta

C23×#88200 #16769559

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC23×#88200

Splittings

FittingC24×Q8×C13 ⋊ C2
SylowC13 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC25C22×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC24×Q8×C13C2
socleC25×C13C23
prime radicalC25×D13C22
hypercenterC24×Q8D13
hypocenterC13C23×C22⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×Q8

14078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076208);