Finite Group Databasebeta

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C52×C11×D13⋊C3 #36339755

order21450
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×C11×D13⋊C3
unambiguous semidirect productD13⋊(C3×C52×C11)
unambiguous semidirect product(C13⋊C3)⋊(C2×C52×C11)
unambiguous semidirect product(C5×D13)⋊(C3×C5×C11)

Splittings

Fitting, socle, HallC52×C11×C13 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C52×C11
HallC52×C11×C13⋊C3 ⋊ C2
HallC52×C11×D13 ⋊ C3
HallC52×C13⋊C3 ⋊ C2×C11
HallC52×D13 ⋊ C3×C11
HallC11×C13⋊C3 ⋊ C2×C52
HallC52×C13 ⋊ C2×C3×C11
HallC11×D13 ⋊ C3×C52
HallC11×C13 ⋊ C2×C3×C52
HallC13⋊C3 ⋊ C2×C52×C11
HallD13 ⋊ C3×C52×C11

Subgroups

subgroupG/H
center, hypercenterC52×C11D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C52×C11
FrattiniC1G
Fitting, socleC52×C11×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C52×C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3575

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 79);