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C3×C3⋊((C11⋊C5)⋊D31) #44501808

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

Aliases

direct productC3×C3⋊((C11⋊C5)⋊D31)
unambiguous semidirect productC3⋊(C3×(C11⋊C5)⋊D31)
unambiguous semidirect product(C11⋊C5)⋊(C3×D93)

Splittings

Fitting, socle, HallC32×C11×C31 ⋊ C2×C5
derivedC3×C11×C31 ⋊ C2×C3×C5
HallC32×C31×C11⋊C5 ⋊ C2
HallC3×D1023 ⋊ C5
HallC31×C11⋊C5 ⋊ C3×D3
HallC32×C11⋊C5 ⋊ D31
HallC11×C31 ⋊ C3×C5×D3
HallC32×C31 ⋊ AGL(1,𝔽11)
HallC32×C11 ⋊ C5×D31
HallC11⋊C5 ⋊ C3×D93
SylowC31 ⋊ C3×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C3×C5×D93
SylowC32 ⋊ (C11⋊C5)⋊D31

Subgroups

subgroupG/H
center, hypercenterC3C3⋊((C11⋊C5)⋊D31)
commutator, cosocle, hypocenterC3×C11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC32×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2046

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 175);