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ΓL(1,𝔽8)×D101⋊C5 #35234607

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

Aliases

direct productΓL(1,𝔽8)×D101⋊C5
unambiguous semidirect productD101⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C101⋊C5)⋊(C2×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×D101)⋊C5
unambiguous semidirect product(C7×D101⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC7×C101 ⋊ C2×C3×C5
HallΓL(1,𝔽8)×C101⋊C5 ⋊ C2
HallC7×D101⋊C5 ⋊ C3
HallΓL(1,𝔽8)×D101 ⋊ C5
HallC7×C101⋊C5 ⋊ C2×C3
HallΓL(1,𝔽8)×C101 ⋊ C2×C5
HallC7×D101 ⋊ C3×C5
HallC101⋊C5 ⋊ C2×ΓL(1,𝔽8)
HallD101 ⋊ C5×ΓL(1,𝔽8)
SylowC101 ⋊ C2×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D101⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C101C2×C3×C5
LCSG ▷ C7×C101
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 707

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 34);