Finite Group Databasebeta

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C7×D1905 #40998686

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

Aliases

direct productC7×D1905
unambiguous semidirect productC3⋊(C7×D635)
unambiguous semidirect productC5⋊(C7×D381)

Splittings

Fitting, socle, HallC3×C5×C7×C127 ⋊ C2
derived, HallC3×C5×C127 ⋊ C2×C7
HallC5×C7×C127 ⋊ D3
HallC3×C7×C127 ⋊ D5
HallC7×C127 ⋊ D15
HallC5×C127 ⋊ D3×C7
HallC3×C127 ⋊ C7×D5
SylowC127 ⋊ C7×D15
HallC3×C5×C7 ⋊ D127
HallC5×C7 ⋊ D381
HallC3×C7 ⋊ D635
HallC3×C5 ⋊ C7×D127
SylowC5 ⋊ C7×D381
SylowC3 ⋊ C7×D635

Subgroups

subgroupG/H
center, hypercenterC7D1905
commutator, cosocle, hypocenterC3×C5×C127C2×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C127C2
LCSG ▷ C3×C5×C127
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13335

Conjugacy classes & character table

6678 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26670, 20);