Finite Group Databasebeta

← Prev (#34086102) Next (#34086104) →

C2×C7⋊C9×ΓL(1,𝔽32) #34086103

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

Aliases

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

Splittings

derived, HallC7×C31 ⋊ C2×C5×C9
HallC2×C31×C7⋊C9 ⋊ C5
HallC2×C7×ΓL(1,𝔽32) ⋊ C9
HallC31×C7⋊C9 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C9
HallC2×C7×C31 ⋊ C5×C9
HallC2×C31 ⋊ C5×C7⋊C9
SylowC31 ⋊ C2×C5×C7⋊C9
HallC2×C7 ⋊ C9×ΓL(1,𝔽32)
SylowC7 ⋊ C2×C9×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×ΓL(1,𝔽32)
commutator, hypocenterC7×C31C2×C5×C9
FrattiniC3C2×ΓL(1,𝔽8)×ΓL(1,𝔽32)
Fitting, socleC2×C3×C7×C31C3×C5
prime radicalC2×C3×C7×ΓL(1,𝔽32)C3
cosocleC3×C7×C31C2×C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3906

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 8);