Finite Group Databasebeta

← Prev (#40999670) Next (#40999672) →

D7×D957 #40999671

order26796
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD7×D957
unambiguous semidirect product(C3×D7)⋊D319
unambiguous semidirect product(C11×D7)⋊D87
unambiguous semidirect product(D7×C29)⋊D33

Splittings

Fitting, socle, derived, HallC3×C7×C11×C29 ⋊ C22
HallC7×C11×C29 ⋊ C2×D3
HallC3×C11×C29 ⋊ C2×D7
HallC3×C7×C29 ⋊ C2×D11
HallC11×C29 ⋊ D3×D7
HallC3×C7×C11 ⋊ C2×D29
HallC7×C29 ⋊ C2×D33
HallC3×C29 ⋊ D7×D11
HallC7×C11 ⋊ C2×D87
HallC3×C11 ⋊ D7×D29
SylowC29 ⋊ D7×D33
HallC3×C7 ⋊ C2×D319
SylowC11 ⋊ D7×D87
SylowC7 ⋊ C2×D957
SylowC3 ⋊ D7×D319

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C29C22
LCSG ▷ C3×C7×C11×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6699

Conjugacy classes & character table

2400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26796, 104);