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C2×#14519870⋊C5 #34086104

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

Aliases

direct productC2×#14519870⋊C5
unambiguous semidirect product(C2×#14519870)⋊C5

Splittings

derived, HallC7×C31 ⋊ C2×C5×C9
HallC2×#14519870 ⋊ C5
HallC2×C7×ΓL(1,𝔽32) ⋊ C9
Hall#14519870 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C9
HallC2×C7×C31 ⋊ C5×C9
HallC2×ΓL(1,𝔽32) ⋊ C7⋊C9
HallΓL(1,𝔽32) ⋊ C2×C7⋊C9
HallC2×C31 ⋊ C5×C7⋊C9
SylowC31 ⋊ C2×C5×C7⋊C9
HallC2×C7 ⋊ ΓL(1,𝔽32)⋊C9
SylowC7 ⋊ C2×ΓL(1,𝔽32)⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3#10620253⋊C5
commutator, hypocenterC7×C31C2×C5×C9
FrattiniC3C2×#10620253⋊C5
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

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 9);