Finite Group Databasebeta

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D3×C11⋊C5×C73 #37562803

order24090
automorphism?
homologyAbelianization (H1) = C2×C5×C73 · Schur multiplier (H2) = C1

Aliases

direct productD3×C11⋊C5×C73
unambiguous semidirect productC3⋊(C2×C11⋊C5×C73)
unambiguous semidirect product(D3×C11)⋊(C5×C73)
unambiguous semidirect product(D3×C11×C73)⋊C5

Splittings

Fitting, socle, HallC3×C11×C73 ⋊ C2×C5
derived, HallC3×C11 ⋊ C2×C5×C73
HallC3×C11⋊C5×C73 ⋊ C2
HallD3×C11×C73 ⋊ C5
HallC11×C73 ⋊ C5×D3
HallC3×C73 ⋊ C2×C11⋊C5
HallC3×C11⋊C5 ⋊ C2×C73
HallD3×C11 ⋊ C5×C73
SylowC11 ⋊ C5×D3×C73
SylowC3 ⋊ C2×C11⋊C5×C73

Subgroups

subgroupG/H
center, hypercenterC73D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C2×C5×C73
FrattiniC1G
Fitting, socleC3×C11×C73C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C73

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2409

Conjugacy classes & character table

1533 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24090, 23);