Finite Group Databasebeta

C23×#88142 #16769609

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

Aliases

direct productC23×#88142

Splittings

SylowC13 ⋊ C23×C4⋊Q8

Subgroups

subgroupG/H
centerC25C22×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC23×C13×C4⋊C4C2
socle, prime radicalC25×C13C23
hypercenterC23×C4⋊C4D13
hypocenterC13C23×C4⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C25 ◁ C23×C4⋊C4

12190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

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, 1076258);