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C17×ΓL(1,𝔽8)⋊#261 #32915484

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)⋊#261
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×#261)

Splittings

Fitting, socle, HallC7×C13×C17 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C17
HallC17×C7⋊#261 ⋊ C3
HallC13×C17×ΓL(1,𝔽8) ⋊ C4
HallC7⋊#261 ⋊ C3×C17
HallC17×ΓL(1,𝔽8) ⋊ #261
HallC13×ΓL(1,𝔽8) ⋊ C4×C17
HallC13×C17 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C17 ⋊ C3×#261
HallΓL(1,𝔽8) ⋊ C17×#261
SylowC13 ⋊ C17×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C17×#261

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)⋊#261
commutator, hypocenterC7×C13C3×C4×C17
FrattiniC1G
Fitting, socleC7×C13×C17C3×C4
prime radicalC17×ΓL(1,𝔽8)×D13C2
cosocleC7×D13C2×C3×C17
LCSG ▷ C7×C13
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1547

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 79);