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ΓL(1,𝔽8)×D767 #44567276

order32214
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D767
unambiguous semidirect productC59⋊(ΓL(1,𝔽8)×D13)

Splittings

Fitting, socle, derived, HallC7×C13×C59 ⋊ C2×C3
HallC13×ΓL(1,𝔽8)×C59 ⋊ C2
HallC7×D767 ⋊ C3
HallΓL(1,𝔽8)×C59 ⋊ D13
HallC13×C59 ⋊ C2×ΓL(1,𝔽8)
HallC7×C59 ⋊ C3×D13
HallC13×ΓL(1,𝔽8) ⋊ D59
HallC7×C13 ⋊ C3×D59
SylowC59 ⋊ ΓL(1,𝔽8)×D13
SylowC13 ⋊ ΓL(1,𝔽8)×D59
SylowC7 ⋊ C3×D767

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C59C2×C3
LCSG ▷ C7×C13×C59
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5369

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32214, 30);