Finite Group Databasebeta

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C11×C5⋊(D79⋊C3) #39907645

order26070
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊(D79⋊C3)
unambiguous semidirect productC5⋊(C11×D79⋊C3)
unambiguous semidirect product(C79⋊C3)⋊(D5×C11)
unambiguous semidirect productD395⋊(C3×C11)
unambiguous semidirect product(C11×D395)⋊C3

Splittings

Fitting, socle, HallC5×C11×C79 ⋊ C2×C3
derived, HallC5×C79 ⋊ C2×C3×C11
HallC5×C11×C79⋊C3 ⋊ C2
HallC11×D395 ⋊ C3
HallC11×C79⋊C3 ⋊ D5
HallC5×C79⋊C3 ⋊ C2×C11
HallC11×C79 ⋊ C3×D5
HallD395 ⋊ C3×C11
HallC79⋊C3 ⋊ D5×C11
SylowC79 ⋊ C3×D5×C11
HallC5×C11 ⋊ D79⋊C3
SylowC5 ⋊ C11×D79⋊C3

Subgroups

subgroupG/H
center, hypercenterC11C5⋊(D79⋊C3)
commutator, cosocle, hypocenterC5×C79C2×C3×C11
FrattiniC1G
Fitting, socleC5×C11×C79C2×C3
LCSG ▷ C5×C79
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4345

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26070, 31);