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C5×ΓL(1,𝔽8)×D127 #40998697

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

Aliases

direct productC5×ΓL(1,𝔽8)×D127

Splittings

Fitting, socle, HallC5×C7×C127 ⋊ C2×C3
derived, HallC7×C127 ⋊ C2×C3×C5
HallC5×ΓL(1,𝔽8)×C127 ⋊ C2
HallC5×C7×D127 ⋊ C3
HallΓL(1,𝔽8)×C127 ⋊ C2×C5
HallC7×D127 ⋊ C3×C5
HallC5×C127 ⋊ C2×ΓL(1,𝔽8)
SylowC127 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D127
SylowC7 ⋊ C3×C5×D127

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D127
commutator, cosocle, hypocenterC7×C127C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C127C2×C3
LCSG ▷ C7×C127
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4445

Conjugacy classes & character table

1625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 31);