Finite Group Databasebeta

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C3×D5×C13×C11⋊C5 #36339727

order21450
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C13×C11⋊C5
unambiguous semidirect productC5⋊(C2×C3×C13×C11⋊C5)
unambiguous semidirect product(D5×C11)⋊(C3×C5×C13)
unambiguous semidirect product(C3×D5×C11)⋊(C5×C13)
unambiguous semidirect product(C3×D5×C11×C13)⋊C5

Splittings

Fitting, socleC3×C5×C11×C13 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C3×C5×C13
HallC3×C5×C13×C11⋊C5 ⋊ C2
HallC5×C13×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ C2×C13
HallC3×C11×C13 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C3×C13
HallC11×C13 ⋊ C3×C5×D5
HallC3×C11 ⋊ C5×D5×C13
SylowC11 ⋊ C3×C5×D5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13D5×C11⋊C5
commutator, cosocle, hypocenterC5×C11C2×C3×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2145

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 51);