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C17×(C7⋊C9)⋊Dic5 #36339191

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

Aliases

direct productC17×(C7⋊C9)⋊Dic5
unambiguous semidirect product(C7⋊C9)⋊(C17×Dic5)
unambiguous semidirect productDic35⋊(C9×C17)
unambiguous semidirect product(C17×Dic35)⋊C9

Splittings

derived, HallC5×C7 ⋊ C4×C9×C17
HallC5×C17×C7⋊C9 ⋊ C4
HallC17×Dic35 ⋊ C9
HallC17×C7⋊C9 ⋊ Dic5
HallC5×C7×C17 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C17
HallDic35 ⋊ C9×C17
HallC7×C17 ⋊ C9×Dic5
HallC5×C17 ⋊ Dic7⋊C9
HallC7⋊C9 ⋊ C17×Dic5
SylowC7 ⋊ C9×C17×Dic5
SylowC5 ⋊ C17×Dic7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C4×C9×C17
FrattiniC2×C3C17×C5⋊AGL(1,𝔽7)
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

1734 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 23);