Finite Group Databasebeta

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C11×D1209 #40998228

order26598
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1209
unambiguous semidirect productC3⋊(C11×D403)
unambiguous semidirect productC13⋊(C11×D93)
unambiguous semidirect productC31⋊(C11×D39)

Splittings

Fitting, socle, HallC3×C11×C13×C31 ⋊ C2
derived, HallC3×C13×C31 ⋊ C2×C11
HallC11×C13×C31 ⋊ D3
HallC3×C11×C31 ⋊ D13
HallC3×C11×C13 ⋊ D31
HallC13×C31 ⋊ D3×C11
HallC11×C31 ⋊ D39
HallC11×C13 ⋊ D93
HallC3×C31 ⋊ C11×D13
HallC3×C13 ⋊ C11×D31
HallC3×C11 ⋊ D403
SylowC31 ⋊ C11×D39
SylowC13 ⋊ C11×D93
SylowC3 ⋊ C11×D403

Subgroups

subgroupG/H
center, hypercenterC11D1209
commutator, cosocle, hypocenterC3×C13×C31C2×C11
FrattiniC1G
Fitting, socleC3×C11×C13×C31C2
LCSG ▷ C3×C13×C31
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13299

Conjugacy classes & character table

6666 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26598, 16);