Finite Group Databasebeta

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C7×D11×#4294 #39911798

order26334
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×D11×#4294
unambiguous semidirect productC11⋊(C2×C7×#4294)

Splittings

derived, HallC11×C19 ⋊ C2×C7×C9
HallC7×C11×#4294 ⋊ C2
HallC7×C19×D11 ⋊ C9
HallC11×#4294 ⋊ C2×C7
HallC7×C11×C19 ⋊ C2×C9
HallC19×D11 ⋊ C7×C9
HallC7×C19 ⋊ C9×D11
HallC7×C11 ⋊ C2×#4294
SylowC19 ⋊ C7×C9×D11
SylowC11 ⋊ C2×C7×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C7D11×C19⋊C3
commutator, hypocenterC11×C19C2×C7×C9
FrattiniC3C7×D11×C19⋊C3
Fitting, socleC3×C7×C11×C19C2×C3
prime radicalC3×C7×C19×D11C3
cosocleC3×C11×C19C2×C3×C7
LCSG ▷ C11×C19
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13167

Conjugacy classes & character table

1323 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26334, 25);