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C5×C11×D219 #37562793

order24090
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D219
unambiguous semidirect productC3⋊(C5×C11×D73)
unambiguous semidirect productC73⋊(C5×D3×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C73 ⋊ C2
derived, HallC3×C73 ⋊ C2×C5×C11
HallC5×C11×C73 ⋊ D3
HallC3×C11×C73 ⋊ C2×C5
HallC3×C5×C73 ⋊ C2×C11
HallC11×C73 ⋊ C5×D3
HallC5×C73 ⋊ D3×C11
HallC3×C5×C11 ⋊ D73
SylowC73 ⋊ C5×D3×C11
HallC3×C11 ⋊ C5×D73
HallC3×C5 ⋊ C11×D73
SylowC3 ⋊ C5×C11×D73

Subgroups

subgroupG/H
center, hypercenterC5×C11D219
commutator, cosocle, hypocenterC3×C73C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C73C2
LCSG ▷ C3×C73
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12045

Conjugacy classes & character table

6105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24090, 13);