Finite Group Databasebeta

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C59×D11⋊C25 #44570088

order32450
automorphism?
homologyAbelianization (H1) = C2×C25×C59 · Schur multiplier (H2) = C1

Aliases

direct productC59×D11⋊C25
unambiguous semidirect productD11⋊(C25×C59)
unambiguous semidirect product(C11⋊C25)⋊(C2×C59)
unambiguous semidirect product(D11×C59)⋊C25

Splittings

derived, SylowC11 ⋊ C2×C25×C59
HallC59×C11⋊C25 ⋊ C2
HallD11×C59 ⋊ C25
HallC11×C59 ⋊ C2×C25
HallC11⋊C25 ⋊ C2×C59
HallD11 ⋊ C25×C59

Subgroups

subgroupG/H
center, hypercenterC5×C59AGL(1,𝔽11)
commutator, hypocenterC11C2×C25×C59
FrattiniC5C59×AGL(1,𝔽11)
Fitting, socleC5×C11×C59C2×C5
prime radicalC5×D11×C59C5
cosocleC5×C11C2×C5×C59
LCSG ▷ C11
UCSC1 ◁ C5×C59

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16225

Conjugacy classes & character table

3245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32450, 11);