Finite Group Databasebeta

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C4×C17×C71⋊C5 #37563274

order24140
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C71⋊C5
unambiguous semidirect product(C4×C71)⋊(C5×C17)
unambiguous semidirect product(C4×C17×C71)⋊C5

Splittings

Fitting, HallC4×C17×C71 ⋊ C5
derived, SylowC71 ⋊ C4×C5×C17
HallC17×C71 ⋊ C4×C5
HallC4×C71 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C71⋊C5
commutator, hypocenterC71C4×C5×C17
FrattiniC2C2×C17×C71⋊C5
FittingC4×C17×C71C5
socleC2×C17×C71C2×C5
prime radicalC2×C17×C71⋊C5C2
cosocleC2×C71C2×C5×C17
LCSG ▷ C71
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4828

Conjugacy classes & character table

1292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24140, 2);