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C2×C5×ΓL(1,𝔽8)×C127 #40998670

order26670
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C127 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C127
unambiguous semidirect product(C2×C7)⋊(C3×C5×C127)
unambiguous semidirect product(C2×C5×C7)⋊(C3×C127)

Splittings

Fitting, socle, HallC2×C5×C7×C127 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C5×C127
HallC5×C7×C127 ⋊ C2×C3
HallC2×C7×C127 ⋊ C3×C5
HallC7×C127 ⋊ C2×C3×C5
HallC2×C5×C7 ⋊ C3×C127
HallC5×C7 ⋊ C2×C3×C127
HallC2×C7 ⋊ C3×C5×C127

Subgroups

subgroupG/H
center, hypercenterC2×C5×C127ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C5×C127
FrattiniC1G
Fitting, socleC2×C5×C7×C127C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C127

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8890

Conjugacy classes & character table

6350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 4);