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C5×C3⋊(D127⋊C7) #40998693

order26670
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(D127⋊C7)
unambiguous semidirect productC3⋊(C5×D127⋊C7)
unambiguous semidirect productD381⋊(C5×C7)
unambiguous semidirect product(C127⋊C7)⋊(C5×D3)
unambiguous semidirect product(C5×D381)⋊C7

Splittings

Fitting, socle, HallC3×C5×C127 ⋊ C2×C7
derived, HallC3×C127 ⋊ C2×C5×C7
HallC3×C5×C127⋊C7 ⋊ C2
HallC5×C127⋊C7 ⋊ D3
HallC5×D381 ⋊ C7
HallC3×C127⋊C7 ⋊ C2×C5
HallC127⋊C7 ⋊ C5×D3
HallD381 ⋊ C5×C7
HallC5×C127 ⋊ D3×C7
SylowC127 ⋊ C5×D3×C7
HallC3×C5 ⋊ D127⋊C7
SylowC3 ⋊ C5×D127⋊C7

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(D127⋊C7)
commutator, cosocle, hypocenterC3×C127C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C127C2×C7
LCSG ▷ C3×C127
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1905

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 27);