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C2×C7×ΓL(1,𝔽32)⋊C9 #34086102

order19530
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×ΓL(1,𝔽32)⋊C9
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C7×C9)
unambiguous semidirect product(C2×C31⋊C9)⋊(C5×C7)
unambiguous semidirect product(C2×C7×C31⋊C9)⋊C5

Splittings

derived, SylowC31 ⋊ C2×C5×C7×C9
HallC2×C7×C31⋊C9 ⋊ C5
HallC2×C7×ΓL(1,𝔽32) ⋊ C9
HallC7×C31⋊C9 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C9
HallC2×C31⋊C9 ⋊ C5×C7
HallC2×C7×C31 ⋊ C5×C9
HallC2×ΓL(1,𝔽32) ⋊ C7×C9
HallC31⋊C9 ⋊ C2×C5×C7
HallC7×C31 ⋊ C2×C5×C9
HallΓL(1,𝔽32) ⋊ C2×C7×C9
HallC2×C31 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7(C31⋊C3)⋊C5
commutator, hypocenterC31C2×C5×C7×C9
FrattiniC3C2×C7×(C31⋊C3)⋊C5
Fitting, socleC2×C3×C7×C31C3×C5
prime radicalC2×C3×C7×ΓL(1,𝔽32)C3
cosocleC3×C31C2×C3×C5×C7
LCSG ▷ C31
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3906

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 7);