Finite Group Databasebeta

C9×D5×D7×C19 #37560997

order23940
automorphism?
homologyAbelianization (H1) = C22×C9×C19 · Schur multiplier (H2) = C2

Aliases

direct productC9×D5×D7×C19

Splittings

Fitting, HallC5×C7×C9×C19 ⋊ C22
derived, HallC5×C7 ⋊ C22×C9×C19
HallC7×C9×C19 ⋊ C2×D5
HallC5×C9×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C22×C9
HallC5×C7×C9 ⋊ C22×C19
HallC7×C19 ⋊ C2×C9×D5
HallC5×C19 ⋊ C2×C9×D7
HallC7×C9 ⋊ C2×D5×C19
HallC5×C9 ⋊ C2×D7×C19
SylowC7 ⋊ C2×C9×D5×C19
SylowC5 ⋊ C2×C9×D7×C19

Subgroups

subgroupG/H
center, hypercenterC9×C19D5×D7
commutator, hypocenterC5×C7C22×C9×C19
FrattiniC3C3×D5×D7×C19
FittingC5×C7×C9×C19C22
socleC3×C5×C7×C19C22×C3
prime radicalC3×D5×D7×C19C3
cosocleC3×C5×C7C22×C3×C19
LCSG ▷ C5×C7
UCSC1 ◁ C9×C19

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 129);