Finite Group Databasebeta

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C5×C17×C127⋊C3 #44569234

order32385
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×C127⋊C3
unambiguous semidirect productC127⋊(C3×C5×C17)
unambiguous semidirect product(C5×C127)⋊(C3×C17)
unambiguous semidirect product(C17×C127)⋊(C3×C5)
unambiguous semidirect product(C5×C17×C127)⋊C3

Splittings

Fitting, socle, HallC5×C17×C127 ⋊ C3
derived, SylowC127 ⋊ C3×C5×C17
HallC17×C127 ⋊ C3×C5
HallC5×C127 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17C127⋊C3
commutator, cosocle, hypocenterC127C3×C5×C17
FrattiniC1G
Fitting, socleC5×C17×C127C3
LCSG ▷ C127
UCSC1 ◁ C5×C17

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10795

Conjugacy classes & character table

3825 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32385, 2);