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C5×ΓL(1,𝔽8)⋊D101 #35234602

order21210
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)⋊D101
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D101)
unambiguous semidirect product(C5×D707)⋊C3

Splittings

Fitting, socle, HallC5×C7×C101 ⋊ C2×C3
derived, HallC7×C101 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C101 ⋊ C2
HallC5×D707 ⋊ C3
HallΓL(1,𝔽8)×C101 ⋊ C2×C5
HallD707 ⋊ C3×C5
HallC5×C101 ⋊ AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ D101
SylowC101 ⋊ C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C3×D101
HallΓL(1,𝔽8) ⋊ C5×D101
SylowC7 ⋊ C3×C5×D101

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)⋊D101
commutator, cosocle, hypocenterC7×C101C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C101C2×C3
LCSG ▷ C7×C101
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3535

Conjugacy classes & character table

1285 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 29);