Finite Group Databasebeta

← Prev (#37587673) Next (#37587675) →

C3×C23×C71⋊C5 #37587674

order24495
automorphism?
homologyAbelianization (H1) = C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×C71⋊C5
unambiguous semidirect productC71⋊(C3×C5×C23)
unambiguous semidirect product(C3×C71)⋊(C5×C23)
unambiguous semidirect product(C23×C71)⋊(C3×C5)
unambiguous semidirect product(C3×C23×C71)⋊C5

Splittings

Fitting, socle, HallC3×C23×C71 ⋊ C5
derived, SylowC71 ⋊ C3×C5×C23
HallC23×C71 ⋊ C3×C5
HallC3×C71 ⋊ C5×C23

Subgroups

subgroupG/H
center, hypercenterC3×C23C71⋊C5
commutator, cosocle, hypocenterC71C3×C5×C23
FrattiniC1G
Fitting, socleC3×C23×C71C5
LCSG ▷ C71
UCSC1 ◁ C3×C23

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4899

Conjugacy classes & character table

1311 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24495, 2);