Finite Group Databasebeta

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C7×D23×D45 #44394396

order28980
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D23×D45
unambiguous semidirect product(C5×D23)⋊(C7×D9)
unambiguous semidirect product(C9×D23)⋊(C7×D5)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C22
derived, HallC5×C9×C23 ⋊ C22×C7
HallC7×C9×C23 ⋊ C2×D5
HallC5×C7×C23 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D23
HallC9×C23 ⋊ C2×C7×D5
HallC7×C23 ⋊ C2×D45
HallC5×C23 ⋊ C2×C7×D9
HallC7×C9 ⋊ D5×D23
HallC5×C9 ⋊ C2×C7×D23
HallC5×C7 ⋊ D9×D23
SylowC23 ⋊ C2×C7×D45
SylowC9 ⋊ C7×D5×D23
SylowC5 ⋊ C7×D9×D23

Subgroups

subgroupG/H
center, hypercenterC7D23×D45
commutator, cosocle, hypocenterC5×C9×C23C22×C7
FrattiniC3C7×D15×D23
FittingC5×C7×C9×C23C22
socleC3×C5×C7×C23C2×D3
LCSG ▷ C5×C9×C23
UCSC1 ◁ C7

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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

2184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 65);