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ΓL(1,𝔽8)×#13184067 #49153141

order37380
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×#13184067
unambiguous semidirect product(C7×#13184067)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C89 ⋊ C3×C4
HallC7×#13184067 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C4
HallΓL(1,𝔽8)×C89 ⋊ AGL(1,𝔽5)
HallC7×C89 ⋊ C3×AGL(1,𝔽5)
HallC5×C89 ⋊ C4×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ #67063
SylowC89 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×#67063
SylowC7 ⋊ C3×#13184067
SylowC5 ⋊ ΓL(1,𝔽8)×#67063

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C89C3×C4
prime radicalΓL(1,𝔽8)×D445C2
cosocleC7×D445C2×C3
LCSG ▷ C5×C7×C89
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3115

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 35);