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C2×C3×C5⋊(D71⋊C7) #44447195

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5⋊(D71⋊C7)
unambiguous semidirect product(C2×C5)⋊(C3×D71⋊C7)
unambiguous semidirect product(C2×C71⋊C7)⋊(C3×D5)
unambiguous semidirect product(C2×D355)⋊(C3×C7)
unambiguous semidirect product(C2×C3×D355)⋊C7

Splittings

Fitting, socleC2×C3×C5×C71 ⋊ C2×C7
derived, HallC5×C71 ⋊ C22×C3×C7
HallC3×C5×C71⋊C7 ⋊ C22
HallC2×C3×D355 ⋊ C7
HallC5×C71⋊C7 ⋊ C22×C3
HallC3×C71⋊C7 ⋊ C2×D5
HallC2×D355 ⋊ C3×C7
HallC3×C5×C71 ⋊ C22×C7
HallC71⋊C7 ⋊ C2×C3×D5
HallC3×C71 ⋊ C2×C7×D5
SylowC71 ⋊ C2×C3×C7×D5
HallC3×C5 ⋊ C2×D71⋊C7
SylowC5 ⋊ C2×C3×D71⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D71⋊C7)
commutator, cosocle, hypocenterC5×C71C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C71C2×C7
LCSG ▷ C5×C71
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2130

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 83);