Finite Group Databasebeta

C23×#88045 #16726508

order3328
isoclinismisoclinic class of #6095
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#88045

Splittings

FittingC23×C42×C13 ⋊ C2
SylowC13 ⋊ C23×#104

Subgroups

subgroupG/H
centerC23×C4D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC23×C42×C13C2
socleC24×C13C22⋊C4
prime radicalC23×#6127C2
cosocleC2×C4×C13C25
hypercenterC23×C42D13
hypocenterC13C23×#104
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C23×C42

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033157);