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C5×C7×C17⋊AGL(1,𝔽7) #38735940

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C17⋊AGL(1,𝔽7)
unambiguous semidirect productC17⋊(C5×C7×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×C7×D17)
unambiguous semidirect productD119⋊(C3×C5×C7)
unambiguous semidirect product(C5×D119)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C72×C17 ⋊ C2×C3
derivedC7×C17 ⋊ C2×C3×C5×C7
HallC5×C7×C17×ΓL(1,𝔽8) ⋊ C2
HallC5×C7×D119 ⋊ C3
HallC7×C17×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×D119 ⋊ C3×C5
HallC72×C17 ⋊ C2×C3×C5
HallC5×C7×ΓL(1,𝔽8) ⋊ D17
HallC5×C72 ⋊ C3×D17
HallC7×ΓL(1,𝔽8) ⋊ C5×D17
HallC5×C17 ⋊ C7×AGL(1,𝔽7)
SylowC72 ⋊ C3×C5×D17
SylowC17 ⋊ C5×C7×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC5×C7C17⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C72×C17C2×C3
LCSG ▷ C7×C17
UCSC1 ◁ C5×C7

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

1645 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 30);