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C2×C5×(C211⋊C3)⋊C5 #44539543

order31650
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC2×C5×(C211⋊C3)⋊C5
unambiguous semidirect product(C2×C211⋊C3)⋊C52
unambiguous semidirect product(C2×C211⋊C5)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C211⋊C3)⋊C5
unambiguous semidirect product(C2×C5×C211⋊C5)⋊C3

Splittings

Fitting, socleC2×C5×C211 ⋊ C3×C5
derived, SylowC211 ⋊ C2×C3×C52
HallC2×C5×C211⋊C5 ⋊ C3
HallC5×C211⋊C5 ⋊ C2×C3
HallC2×C211⋊C3 ⋊ C52
HallC211⋊C3 ⋊ C2×C52
HallC2×C211 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC2×C5(C211⋊C3)⋊C5
commutator, cosocle, hypocenterC211C2×C3×C52
FrattiniC1G
Fitting, socleC2×C5×C211C3×C5
LCSG ▷ C211
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2110

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31650, 23);