Finite Group Databasebeta

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C5×(C103⋊C3)⋊C17 #39911035

order26265
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C103⋊C3)⋊C17
unambiguous semidirect product(C103⋊C3)⋊(C5×C17)
unambiguous semidirect product(C5×C103⋊C3)⋊C17
unambiguous semidirect product(C103⋊C17)⋊(C3×C5)
unambiguous semidirect product(C5×C103⋊C17)⋊C3

Splittings

Fitting, socle, HallC5×C103 ⋊ C3×C17
derived, SylowC103 ⋊ C3×C5×C17
HallC5×C103⋊C17 ⋊ C3
HallC103⋊C17 ⋊ C3×C5
HallC5×C103⋊C3 ⋊ C17
HallC103⋊C3 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC5(C103⋊C3)⋊C17
commutator, cosocle, hypocenterC103C3×C5×C17
FrattiniC1G
Fitting, socleC5×C103C3×C17
LCSG ▷ C103
UCSC1 ◁ C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 515

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26265, 4);