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C7×ΓL(1,𝔽8)×D85 #38735958

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

Aliases

direct productC7×ΓL(1,𝔽8)×D85
unambiguous semidirect productC5⋊(C7×ΓL(1,𝔽8)×D17)
unambiguous semidirect productC17⋊(C7×D5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D85)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C72×C17 ⋊ C2×C3
derivedC5×C7×C17 ⋊ C2×C3×C7
HallC5×C7×C17×ΓL(1,𝔽8) ⋊ C2
HallC72×D85 ⋊ C3
HallC7×C17×ΓL(1,𝔽8) ⋊ D5
HallC72×C17 ⋊ C3×D5
HallC5×C7×ΓL(1,𝔽8) ⋊ D17
HallC5×C72 ⋊ C3×D17
HallC5×C17 ⋊ C2×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C3×D85
SylowC17 ⋊ C7×D5×ΓL(1,𝔽8)
SylowC5 ⋊ C7×ΓL(1,𝔽8)×D17

Subgroups

subgroupG/H
center, hypercenterC7ΓL(1,𝔽8)×D85
commutator, cosocle, hypocenterC5×C7×C17C2×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C17C2×C3
LCSG ▷ C5×C7×C17
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1785

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 48);