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C3×C17×AGL(1,𝔽5)×ΓL(1,𝔽8) #36339345

order21420
automorphism?
homologyAbelianization (H1) = C32×C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×AGL(1,𝔽5)×ΓL(1,𝔽8)
unambiguous semidirect product(C7×AGL(1,𝔽5))⋊(C32×C17)
unambiguous semidirect product(C3×C7×AGL(1,𝔽5))⋊(C3×C17)
unambiguous semidirect product(C7×C17×AGL(1,𝔽5))⋊C32
unambiguous semidirect product(C3×C7×C17×AGL(1,𝔽5))⋊C3

Splittings

Fitting, socleC3×C5×C7×C17 ⋊ C3×C4
derived, HallC5×C7 ⋊ C32×C4×C17
HallC3×C5×C17×ΓL(1,𝔽8) ⋊ C4
HallC7×C17×AGL(1,𝔽5) ⋊ C32
HallC5×C7×C17 ⋊ C32×C4
HallC3×C5×ΓL(1,𝔽8) ⋊ C4×C17
HallC7×AGL(1,𝔽5) ⋊ C32×C17
HallC7×C17 ⋊ C32×AGL(1,𝔽5)
HallC5×C17 ⋊ C3×C4×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C17×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×C17×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C17AGL(1,𝔽5)×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C32×C4×C17
FrattiniC1G
Fitting, socleC3×C5×C7×C17C3×C4
prime radicalC3×D5×C17×ΓL(1,𝔽8)C2
cosocleC7×D5C2×C32×C17
LCSG ▷ C5×C7
UCSC1 ◁ C3×C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1785

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 177);