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C7×A4×C71⋊C5 #44447191

order29820
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×A4×C71⋊C5
unambiguous semidirect productC22⋊(C3×C7×C71⋊C5)
unambiguous semidirect product(C7×A4×C71)⋊C5

Splittings

Fitting, socle, HallC22×C7×C71 ⋊ C3×C5
derived, HallC22×C71 ⋊ C3×C5×C7
HallC22×C7×C71⋊C5 ⋊ C3
HallC7×A4×C71 ⋊ C5
HallC22×C71⋊C5 ⋊ C3×C7
HallA4×C71 ⋊ C5×C7
HallC7×C71 ⋊ C5×A4
SylowC71 ⋊ C5×C7×A4
HallC22×C7 ⋊ C3×C71⋊C5
SylowC22 ⋊ C3×C7×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC7A4×C71⋊C5
commutator, cosocle, hypocenterC22×C71C3×C5×C7
FrattiniC1G
Fitting, socleC22×C7×C71C3×C5
LCSG ▷ C22×C71
UCSC1 ◁ C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1988

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 79);