Finite Group Databasebeta

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C5×D7×D9×C23 #44394388

order28980
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC5×D7×D9×C23
unambiguous semidirect product(C7×D9)⋊(C2×C5×C23)
unambiguous semidirect product(C9×D7)⋊(C2×C5×C23)
unambiguous semidirect productD63⋊(C2×C5×C23)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C22
derived, HallC7×C9 ⋊ C22×C5×C23
HallC7×C9×C23 ⋊ C22×C5
HallC5×C9×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D9
HallC5×C7×C9 ⋊ C22×C23
HallC9×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C2×C5×D9
HallC5×C9 ⋊ C2×D7×C23
HallC5×C7 ⋊ C2×D9×C23
SylowC9 ⋊ C2×C5×D7×C23
SylowC7 ⋊ C2×C5×D9×C23

Subgroups

subgroupG/H
center, hypercenterC5×C23D7×D9
commutator, cosocle, hypocenterC7×C9C22×C5×C23
FrattiniC3C5×D3×D7×C23
FittingC5×C7×C9×C23C22
socleC3×C5×C7×C23C2×D3
LCSG ▷ C7×C9
UCSC1 ◁ C5×C23

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 7245

Conjugacy classes & character table

3450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 57);