Finite Group Databasebeta

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C5×C7×A4×C71 #44447271

order29820
automorphism?
homologyAbelianization (H1) = C3×C5×C7×C71 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×A4×C71
unambiguous semidirect productC22⋊(C3×C5×C7×C71)
unambiguous semidirect product(C22×C5)⋊(C3×C7×C71)

Splittings

Fitting, socle, HallC22×C5×C7×C71 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C7×C71
HallC22×C7×C71 ⋊ C3×C5
HallC22×C5×C71 ⋊ C3×C7
HallC22×C71 ⋊ C3×C5×C7
HallC22×C5×C7 ⋊ C3×C71
HallC22×C7 ⋊ C3×C5×C71
HallC22×C5 ⋊ C3×C7×C71

Subgroups

subgroupG/H
center, hypercenterC5×C7×C71A4
commutator, cosocle, hypocenterC22C3×C5×C7×C71
FrattiniC1G
Fitting, socleC22×C5×C7×C71C3
LCSG ▷ C22
UCSC1 ◁ C5×C7×C71

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9940

Conjugacy classes & character table

9940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 159);