Finite Group Databasebeta

← Prev (#38735940) Next (#38735942) →

C5×C17×ΓL(1,𝔽8)⋊D7 #38735941

order24990
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×ΓL(1,𝔽8)⋊D7
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D7×C17)

Splittings

Fitting, socle, HallC5×C72×C17 ⋊ C2×C3
derived, SylowC72 ⋊ C2×C3×C5×C17
HallC5×C7×C17×ΓL(1,𝔽8) ⋊ C2
HallC5×C17×C7⋊D7 ⋊ C3
HallC7×C17×ΓL(1,𝔽8) ⋊ C2×C5
HallC17×C7⋊D7 ⋊ C3×C5
HallC72×C17 ⋊ C2×C3×C5
HallC5×C7×ΓL(1,𝔽8) ⋊ C2×C17
HallC5×C7⋊D7 ⋊ C3×C17
HallC5×C72 ⋊ C2×C3×C17
HallC7×ΓL(1,𝔽8) ⋊ C2×C5×C17
HallC7⋊D7 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17ΓL(1,𝔽8)⋊D7
commutator, cosocle, hypocenterC72C2×C3×C5×C17
FrattiniC1G
Fitting, socleC5×C72×C17C2×C3
LCSG ▷ C72
UCSC1 ◁ C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1785

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 31);