Finite Group Databasebeta

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C2×C5×C11⋊C5×C59 #44570098

order32450
automorphism?
homologyAbelianization (H1) = C2×C52×C59 · Schur multiplier (H2) = C5

Aliases

direct productC2×C5×C11⋊C5×C59
unambiguous semidirect product(C2×C11)⋊(C52×C59)
unambiguous semidirect product(C2×C5×C11)⋊(C5×C59)
unambiguous semidirect product(C2×C11×C59)⋊C52
unambiguous semidirect product(C2×C5×C11×C59)⋊C5

Splittings

Fitting, socleC2×C5×C11×C59 ⋊ C5
derived, SylowC11 ⋊ C2×C52×C59
HallC2×C11×C59 ⋊ C52
HallC11×C59 ⋊ C2×C52
HallC2×C11 ⋊ C52×C59

Subgroups

subgroupG/H
center, hypercenterC2×C5×C59C11⋊C5
commutator, cosocle, hypocenterC11C2×C52×C59
FrattiniC1G
Fitting, socleC2×C5×C11×C59C5
LCSG ▷ C11
UCSC1 ◁ C2×C5×C59

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6490

Conjugacy classes & character table

4130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32450, 21);