Finite Group Databasebeta

← Prev (#44394333) Next (#44394335) →

C5×C7×C9×Dic23 #44394334

order28980
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C9×Dic23
unambiguous semidirect productC23⋊(C4×C5×C7×C9)

Splittings

derived, SylowC23 ⋊ C4×C5×C7×C9
HallC5×C7×C9×C23 ⋊ C4
HallC7×C9×C23 ⋊ C4×C5
HallC5×C9×C23 ⋊ C4×C7
HallC5×C7×C23 ⋊ C4×C9
HallC9×C23 ⋊ C4×C5×C7
HallC7×C23 ⋊ C4×C5×C9
HallC5×C23 ⋊ C4×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C9D23
commutator, hypocenterC23C4×C5×C7×C9
FrattiniC2×C3C3×C5×C7×D23
FittingC2×C5×C7×C9×C23C2
socle, prime radicalC2×C3×C5×C7×C23C2×C3
cosocleC2×C3×C23C2×C3×C5×C7
LCSG ▷ C23
UCSC1 ◁ C2×C5×C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 3);