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C5×(C11⋊C5)⋊D59 #44570092

order32450
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×(C11⋊C5)⋊D59
unambiguous semidirect product(C11⋊C5)⋊(C5×D59)
unambiguous semidirect productC59⋊(C5×AGL(1,𝔽11))
unambiguous semidirect productD649⋊C52
unambiguous semidirect product(C5×D649)⋊C5

Splittings

Fitting, socleC5×C11×C59 ⋊ C2×C5
derived, HallC11×C59 ⋊ C2×C52
HallC5×C11⋊C5×C59 ⋊ C2
HallD649 ⋊ C52
HallC5×C11⋊C5 ⋊ D59
SylowC59 ⋊ C5×AGL(1,𝔽11)
SylowC11 ⋊ C52×D59

Subgroups

subgroupG/H
center, hypercenterC5(C11⋊C5)⋊D59
commutator, cosocle, hypocenterC11×C59C2×C52
FrattiniC1G
Fitting, socleC5×C11×C59C2×C5
LCSG ▷ C11×C59
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3245

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32450, 15);