Finite Group Databasebeta

C23×#88048 #16726560

order3328
isoclinismisoclinic class of #6104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#88048

Splittings

SylowC13 ⋊ C23×#106

Subgroups

subgroupG/H
centerC25C22⋊D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC23×C13×C4⋊C4C2
socle, prime radicalC25×C13D4
cosocleC2×C4×C13C25
hypercenterC23×C4⋊C4D13
hypocenterC13C23×#106
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

3614 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, 1033209);