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C5×(C43⋊C3)⋊C7 #17985263

order4515
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C43⋊C3)⋊C7
unambiguous semidirect product(C43⋊C3)⋊(C5×C7)
unambiguous semidirect product(C43⋊C7)⋊(C3×C5)
unambiguous semidirect product(C5×C43⋊C3)⋊C7
unambiguous semidirect product(C5×C43⋊C7)⋊C3

Splittings

Fitting, socle, HallC5×C43 ⋊ C3×C7
derived, SylowC43 ⋊ C3×C5×C7
HallC5×C43⋊C7 ⋊ C3
HallC5×C43⋊C3 ⋊ C7
HallC43⋊C7 ⋊ C3×C5
HallC43⋊C3 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC5(C43⋊C3)⋊C7
commutator, cosocle, hypocenterC43C3×C5×C7
FrattiniC1G
Fitting, socleC5×C43C3×C7
LCSG ▷ C43
UCSC1 ◁ C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 215

Conjugacy classes & character table

115 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×(C43⋊C3)⋊C7, C5×C22⋊((C43⋊C3)⋊C7), C25×(C43⋊C3)⋊C7, …
maximal normal subgroup ofC3×C5×(C43⋊C3)⋊C7, C25×(C43⋊C3)⋊C7, C52×(C43⋊C3)⋊C7, …
maximal quotient ofC5×(C43⋊C7)⋊C9, C3×C5×(C43⋊C3)⋊C7, C5×C22⋊((C43⋊C3)⋊C7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4515, 7);