Finite Group Databasebeta

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D33×(C31⋊C3)⋊C5 #44501772

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productD33×(C31⋊C3)⋊C5
unambiguous semidirect productC3⋊(D11×(C31⋊C3)⋊C5)
unambiguous semidirect product(D33×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socle, derivedC3×C11×C31 ⋊ C2×C3×C5
HallC3×C11×(C31⋊C3)⋊C5 ⋊ C2
HallD33×C31⋊C3 ⋊ C5
HallC3×C11×C31⋊C3 ⋊ C2×C5
HallC11×ΓL(1,𝔽32) ⋊ C3×D3
HallC3×(C31⋊C3)⋊C5 ⋊ D11
HallC11×C31 ⋊ C3×C5×D3
HallC3×C31⋊C3 ⋊ C5×D11
HallΓL(1,𝔽32) ⋊ C3×D33
SylowC31 ⋊ C3×C5×D33
SylowC11 ⋊ D3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C31C2×C3×C5
LCSG ▷ C3×C11×C31
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1023

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 139);