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C2×C3×#10620253⋊C5 #34086210

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×#10620253⋊C5
unambiguous semidirect product(C2×C3×#10620253)⋊C5

Splittings

Fitting, socleC2×C3×C7×C31 ⋊ C3×C5
derived, HallC7×C31 ⋊ C2×C32×C5
HallC2×C3×#10620253 ⋊ C5
HallC2×C7×ΓL(1,𝔽32) ⋊ C32
HallC3×#10620253 ⋊ C2×C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C32
HallC2×C7×C31 ⋊ C32×C5
HallC2×ΓL(1,𝔽32) ⋊ C3×ΓL(1,𝔽8)
HallΓL(1,𝔽32) ⋊ C2×C3×ΓL(1,𝔽8)
HallC2×C31 ⋊ C3×C5×ΓL(1,𝔽8)
SylowC31 ⋊ C2×C3×C5×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×(C31⋊C3)⋊C5
SylowC7 ⋊ C2×C3×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3#10620253⋊C5
commutator, cosocle, hypocenterC7×C31C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C7×C31C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1302

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, 115);