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C2×(C571⋊C3)⋊C5 #30686170

order17130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×(C571⋊C3)⋊C5
unambiguous semidirect product(C2×C571⋊C3)⋊C5
unambiguous semidirect product(C2×C571⋊C5)⋊C3

Splittings

Fitting, socle, HallC2×C571 ⋊ C3×C5
derived, SylowC571 ⋊ C2×C3×C5
HallC2×C571⋊C5 ⋊ C3
HallC2×C571⋊C3 ⋊ C5
HallC571⋊C5 ⋊ C2×C3
HallC571⋊C3 ⋊ C2×C5

Subgroups

subgroupG/H
center, hypercenterC2(C571⋊C3)⋊C5
commutator, cosocle, hypocenterC571C2×C3×C5
FrattiniC1G
Fitting, socleC2×C571C3×C5
LCSG ▷ C571
UCSC1 ◁ C2

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1142

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×(C571⋊C3)⋊C5, ((C571⋊C3)⋊C4)⋊C5, C2×(D571⋊C3)⋊C5, …
maximal normal subgroup ofC4×(C571⋊C3)⋊C5, ((C571⋊C3)⋊C4)⋊C5, C2×(D571⋊C3)⋊C5, …
maximal quotient ofC4×(C571⋊C3)⋊C5, C22×(C571⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17130, 4);