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D5×ΓL(1,𝔽8)×C101 #35234603

order21210
automorphism?
homologyAbelianization (H1) = C2×C3×C101 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽8)×C101
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C101)
unambiguous semidirect product(C7×D5)⋊(C3×C101)
unambiguous semidirect product(C7×D5×C101)⋊C3

Splittings

Fitting, socle, HallC5×C7×C101 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C101
HallC5×ΓL(1,𝔽8)×C101 ⋊ C2
HallC7×D5×C101 ⋊ C3
HallC7×C101 ⋊ C3×D5
HallC5×C101 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×C101
HallC7×D5 ⋊ C3×C101
SylowC7 ⋊ C3×D5×C101
SylowC5 ⋊ C2×ΓL(1,𝔽8)×C101

Subgroups

subgroupG/H
center, hypercenterC101D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C101
FrattiniC1G
Fitting, socleC5×C7×C101C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C101

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3535

Conjugacy classes & character table

2020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21210, 30);