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C3×C4×(C71⋊C5)⋊C7 #44447116

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×(C71⋊C5)⋊C7
unambiguous semidirect product(C4×C71⋊C5)⋊(C3×C7)
unambiguous semidirect product(C4×C71⋊C7)⋊(C3×C5)
unambiguous semidirect product(C3×C4×C71⋊C5)⋊C7
unambiguous semidirect product(C3×C4×C71⋊C7)⋊C5

Splittings

Fitting, HallC3×C4×C71 ⋊ C5×C7
derived, SylowC71 ⋊ C3×C4×C5×C7
HallC3×C4×C71⋊C7 ⋊ C5
HallC3×C4×C71⋊C5 ⋊ C7
HallC4×C71⋊C7 ⋊ C3×C5
HallC3×C71⋊C7 ⋊ C4×C5
HallC4×C71⋊C5 ⋊ C3×C7
HallC3×C71⋊C5 ⋊ C4×C7
HallC71⋊C7 ⋊ C3×C4×C5
HallC71⋊C5 ⋊ C3×C4×C7
HallC4×C71 ⋊ C3×C5×C7
HallC3×C71 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4(C71⋊C5)⋊C7
commutator, hypocenterC71C3×C4×C5×C7
FrattiniC2C2×C3×(C71⋊C5)⋊C7
FittingC3×C4×C71C5×C7
socleC2×C3×C71C2×C5×C7
prime radicalC2×C3×(C71⋊C5)⋊C7C2
cosocleC2×C71C2×C3×C5×C7
LCSG ▷ C71
UCSC1 ◁ C3×C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 852

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 4);