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ΓL(1,𝔽8)×D485 #35205040

order20370
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D485
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D97)

Splittings

Fitting, socle, derived, HallC5×C7×C97 ⋊ C2×C3
HallC5×ΓL(1,𝔽8)×C97 ⋊ C2
HallC7×D485 ⋊ C3
HallΓL(1,𝔽8)×C97 ⋊ D5
HallC7×C97 ⋊ C3×D5
HallC5×C97 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ D97
SylowC97 ⋊ D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D97
SylowC7 ⋊ C3×D485
SylowC5 ⋊ ΓL(1,𝔽8)×D97

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C97C2×C3
LCSG ▷ C5×C7×C97
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3395

Conjugacy classes & character table

1220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20370, 38);