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C2×C13⋊C3×C11⋊C5 #16864239

order4290
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C13⋊C3×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C5×C13⋊C3)
unambiguous semidirect product(C2×C13)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×C11×C13⋊C3)⋊C5
unambiguous semidirect product(C2×C13×C11⋊C5)⋊C3

Splittings

Fitting, socle, HallC2×C11×C13 ⋊ C3×C5
derived, HallC11×C13 ⋊ C2×C3×C5
HallC2×C13×C11⋊C5 ⋊ C3
HallC2×C11×C13⋊C3 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×C3
HallC11×C13⋊C3 ⋊ C2×C5
HallC2×C13 ⋊ C3×C11⋊C5
HallC2×C11 ⋊ C5×C13⋊C3
SylowC13 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C2×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×C11⋊C5
commutator, cosocle, hypocenterC11×C13C2×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C13C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 286

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2)(4,5,7)(6,9,12)(8,11,10)(13,15,14)(17,18,20,23,22)(19,21,25,26,24);(3,4,6,5,8,12,9,13,15,7,10,14,11)(16,17,19,22,18,20,24,26,21,23,25)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C13⋊C3×C11⋊C5, C2×C3×C13⋊C3×C11⋊C5, D5×C13⋊C3×C11⋊C5, …
maximal normal subgroup ofC2×C3×C13⋊C3×C11⋊C5, C2×C5×C13⋊C3×C11⋊C5, C2×C7×C13⋊C3×C11⋊C5
maximal quotient ofC2×C11⋊C5×C13⋊C9, D3×C13⋊C3×C11⋊C5, C2×C3×C13⋊C3×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 4);