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C2×C3×C5×ΓL(1,𝔽8)×C31 #34086287

order19530
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C31 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×ΓL(1,𝔽8)×C31
unambiguous semidirect product(C2×C7)⋊(C32×C5×C31)
unambiguous semidirect product(C2×C3×C7)⋊(C3×C5×C31)
unambiguous semidirect product(C2×C5×C7)⋊(C32×C31)
unambiguous semidirect product(C2×C3×C5×C7)⋊(C3×C31)

Splittings

Fitting, socleC2×C3×C5×C7×C31 ⋊ C3
derived, SylowC7 ⋊ C2×C32×C5×C31
HallC2×C5×C7×C31 ⋊ C32
HallC5×C7×C31 ⋊ C2×C32
HallC2×C7×C31 ⋊ C32×C5
HallC7×C31 ⋊ C2×C32×C5
HallC2×C5×C7 ⋊ C32×C31
HallC5×C7 ⋊ C2×C32×C31
HallC2×C7 ⋊ C32×C5×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C31ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C32×C5×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C31C3
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C31

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6510

Conjugacy classes & character table

4650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19530, 192);