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C5×C7⋊C9×Dic17 #36339186

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

Aliases

direct productC5×C7⋊C9×Dic17
unambiguous semidirect product(C7×Dic17)⋊(C5×C9)
unambiguous semidirect product(C5×C7×Dic17)⋊C9

Splittings

derived, HallC7×C17 ⋊ C4×C5×C9
HallC5×C17×C7⋊C9 ⋊ C4
HallC5×C7×Dic17 ⋊ C9
HallC17×C7⋊C9 ⋊ C4×C5
HallC5×C7×C17 ⋊ C4×C9
HallC7×Dic17 ⋊ C5×C9
HallC5×C17 ⋊ C4×C7⋊C9
HallC5×C7 ⋊ C9×Dic17
SylowC17 ⋊ C4×C5×C7⋊C9
SylowC7 ⋊ C5×C9×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5ΓL(1,𝔽8)×D17
commutator, hypocenterC7×C17C4×C5×C9
FrattiniC2×C3C5×ΓL(1,𝔽8)×D17
Fitting, socle, prime radicalC2×C3×C5×C7×C17C2×C3
cosocleC2×C3×C7×C17C2×C3×C5
LCSG ▷ C7×C17
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 18);