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ΓL(1,𝔽32)×C3⋊D33 #44501844

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

Aliases

direct productΓL(1,𝔽32)×C3⋊D33
unambiguous semidirect productC3⋊(D33×ΓL(1,𝔽32))

Splittings

Fitting, socle, derived, HallC32×C11×C31 ⋊ C2×C5
HallC32×C11×ΓL(1,𝔽32) ⋊ C2
HallC31×C3⋊D33 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ C3⋊D3
HallC32×ΓL(1,𝔽32) ⋊ D11
HallC11×C31 ⋊ C5×C3⋊D3
HallC32×C31 ⋊ C5×D11
HallC32×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C3⋊D33
SylowC11 ⋊ C3⋊D3×ΓL(1,𝔽32)
SylowC32 ⋊ D11×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C31C2×C5
LCSG ▷ C32×C11×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 211);