Finite Group Databasebeta

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D5×C11⋊C5×C59 #44570096

order32450
automorphism?
homologyAbelianization (H1) = C2×C5×C59 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11⋊C5×C59
unambiguous semidirect productC5⋊(C2×C11⋊C5×C59)
unambiguous semidirect product(D5×C11)⋊(C5×C59)
unambiguous semidirect product(D5×C11×C59)⋊C5

Splittings

Fitting, socleC5×C11×C59 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C5×C59
HallC5×C11⋊C5×C59 ⋊ C2
HallC11×C59 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C59
SylowC11 ⋊ C5×D5×C59

Subgroups

subgroupG/H
center, hypercenterC59D5×C11⋊C5
commutator, cosocle, hypocenterC5×C11C2×C5×C59
FrattiniC1G
Fitting, socleC5×C11×C59C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C59

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3245

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32450, 19);