Finite Group Databasebeta

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C5×C7×C17×Dic9 #36339178

order21420
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C17×Dic9
unambiguous semidirect productC9⋊(C4×C5×C7×C17)

Splittings

derived, SylowC9 ⋊ C4×C5×C7×C17
HallC5×C7×C9×C17 ⋊ C4
HallC7×C9×C17 ⋊ C4×C5
HallC5×C9×C17 ⋊ C4×C7
HallC5×C7×C9 ⋊ C4×C17
HallC9×C17 ⋊ C4×C5×C7
HallC7×C9 ⋊ C4×C5×C17
HallC5×C9 ⋊ C4×C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C17D9
commutator, hypocenterC9C4×C5×C7×C17
FrattiniC2×C3C5×D3×C7×C17
FittingC2×C5×C7×C9×C17C2
socle, prime radicalC2×C3×C5×C7×C17D3
cosocleC2×C9C2×C5×C7×C17
LCSG ▷ C9
UCSC1 ◁ C2×C5×C7×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

7140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 10);