Finite Group Databasebeta

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C3×D35×C127 #40998679

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

Aliases

direct productC3×D35×C127
unambiguous semidirect productC5⋊(C3×D7×C127)

Splittings

Fitting, socle, HallC3×C5×C7×C127 ⋊ C2
derived, HallC5×C7 ⋊ C2×C3×C127
HallC5×C7×C127 ⋊ C2×C3
HallC3×C7×C127 ⋊ D5
HallC3×C5×C127 ⋊ D7
HallC7×C127 ⋊ C3×D5
HallC5×C127 ⋊ C3×D7
HallC3×C5×C7 ⋊ C2×C127
HallC3×C7 ⋊ D5×C127
HallC3×C5 ⋊ D7×C127
SylowC7 ⋊ C3×D5×C127
SylowC5 ⋊ C3×D7×C127

Subgroups

subgroupG/H
center, hypercenterC3×C127D35
commutator, cosocle, hypocenterC5×C7C2×C3×C127
FrattiniC1G
Fitting, socleC3×C5×C7×C127C2
LCSG ▷ C5×C7
UCSC1 ◁ C3×C127

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13335

Conjugacy classes & character table

7239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 13);