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C5×ΓL(1,𝔽8)⋊D173 #49138105

order36330
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊D173
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D173)
unambiguous semidirect productC173⋊(C5×AGL(1,𝔽7))
unambiguous semidirect productD1211⋊(C3×C5)
unambiguous semidirect product(C5×D1211)⋊C3

Splittings

Fitting, socle, HallC5×C7×C173 ⋊ C2×C3
derived, HallC7×C173 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C173 ⋊ C2
HallC5×D1211 ⋊ C3
HallΓL(1,𝔽8)×C173 ⋊ C2×C5
HallD1211 ⋊ C3×C5
HallC5×C173 ⋊ AGL(1,𝔽7)
SylowC173 ⋊ C5×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ D173
HallC5×C7 ⋊ C3×D173
HallΓL(1,𝔽8) ⋊ C5×D173
SylowC7 ⋊ C3×C5×D173

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊D173
commutator, cosocle, hypocenterC7×C173C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C173C2×C3
LCSG ▷ C7×C173
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6055

Conjugacy classes & character table

2185 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36330, 20);