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C17×Dic5×C7⋊C9 #36339189

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

Aliases

direct productC17×Dic5×C7⋊C9
unambiguous semidirect product(C7×Dic5)⋊(C9×C17)
unambiguous semidirect product(C7×C17×Dic5)⋊C9

Splittings

derived, HallC5×C7 ⋊ C4×C9×C17
HallC5×C17×C7⋊C9 ⋊ C4
HallC7×C17×Dic5 ⋊ C9
HallC5×C7×C17 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C17
HallC7×Dic5 ⋊ C9×C17
HallC7×C17 ⋊ C9×Dic5
HallC5×C17 ⋊ C4×C7⋊C9
SylowC7 ⋊ C9×C17×Dic5
SylowC5 ⋊ C4×C17×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C4×C9×C17
FrattiniC2×C3D5×C17×ΓL(1,𝔽8)
Fitting, socle, prime radicalC2×C3×C5×C7×C17C2×C3
cosocleC2×C3×C5×C7C2×C3×C17
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 21);