Finite Group Databasebeta

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C4×C5×C17×C7⋊C9 #36339170

order21420
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C17×C7⋊C9
unambiguous semidirect product(C4×C7)⋊(C5×C9×C17)
unambiguous semidirect product(C4×C5×C7)⋊(C9×C17)
unambiguous semidirect product(C4×C7×C17)⋊(C5×C9)
unambiguous semidirect product(C4×C5×C7×C17)⋊C9

Splittings

derived, SylowC7 ⋊ C4×C5×C9×C17
HallC4×C5×C7×C17 ⋊ C9
HallC5×C7×C17 ⋊ C4×C9
HallC4×C7×C17 ⋊ C5×C9
HallC4×C5×C7 ⋊ C9×C17
HallC7×C17 ⋊ C4×C5×C9
HallC5×C7 ⋊ C4×C9×C17
HallC4×C7 ⋊ C5×C9×C17

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C17ΓL(1,𝔽8)
commutator, hypocenterC7C4×C5×C9×C17
FrattiniC2×C3C2×C5×C17×ΓL(1,𝔽8)
FittingC3×C4×C5×C7×C17C3
socle, prime radicalC2×C3×C5×C7×C17C2×C3
cosocleC2×C3×C7C2×C3×C5×C17
LCSG ▷ C7
UCSC1 ◁ C3×C4×C5×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

5100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 2);