Finite Group Databasebeta

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C5×C9×Dic161 #44394336

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

Aliases

direct productC5×C9×Dic161
unambiguous semidirect productC23⋊(C5×C9×Dic7)

Splittings

derived, HallC7×C23 ⋊ C4×C5×C9
HallC5×C7×C9×C23 ⋊ C4
HallC7×C9×C23 ⋊ C4×C5
HallC5×C9×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ C4×C9
HallC5×C7×C9 ⋊ Dic23
HallC9×C23 ⋊ C5×Dic7
HallC5×C23 ⋊ C9×Dic7
HallC7×C9 ⋊ C5×Dic23
HallC5×C7 ⋊ C9×Dic23
SylowC23 ⋊ C5×C9×Dic7
SylowC7 ⋊ C5×C9×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D161
commutator, hypocenterC7×C23C4×C5×C9
FrattiniC2×C3C3×C5×D161
FittingC2×C5×C7×C9×C23C2
socle, prime radicalC2×C3×C5×C7×C23C2×C3
cosocleC2×C3×C7×C23C2×C3×C5
LCSG ▷ C7×C23
UCSC1 ◁ C2×C5×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

7380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 5);