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C2×C7×(C151⋊C3)⋊C5 #44540238

order31710
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×(C151⋊C3)⋊C5
unambiguous semidirect product(C2×C151⋊C3)⋊(C5×C7)
unambiguous semidirect product(C2×C151⋊C5)⋊(C3×C7)
unambiguous semidirect product(C2×C7×C151⋊C3)⋊C5

Splittings

Fitting, socle, HallC2×C7×C151 ⋊ C3×C5
derived, SylowC151 ⋊ C2×C3×C5×C7
HallC2×C7×C151⋊C5 ⋊ C3
HallC2×C7×C151⋊C3 ⋊ C5
HallC7×C151⋊C5 ⋊ C2×C3
HallC7×C151⋊C3 ⋊ C2×C5
HallC2×C151⋊C5 ⋊ C3×C7
HallC7×C151 ⋊ C2×C3×C5
HallC2×C151⋊C3 ⋊ C5×C7
HallC151⋊C5 ⋊ C2×C3×C7
HallC151⋊C3 ⋊ C2×C5×C7
HallC2×C151 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7(C151⋊C3)⋊C5
commutator, cosocle, hypocenterC151C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C7×C151C3×C5
LCSG ▷ C151
UCSC1 ◁ C2×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2114

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 7);