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C3×D13×C11⋊C5 #16864255

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

Aliases

direct productC3×D13×C11⋊C5
unambiguous semidirect product(C3×C11×D13)⋊C5

Splittings

Fitting, socle, HallC3×C11×C13 ⋊ C2×C5
derived, HallC11×C13 ⋊ C2×C3×C5
HallC3×C13×C11⋊C5 ⋊ C2
HallC3×C11×D13 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×C3
HallC11×D13 ⋊ C3×C5
HallC3×C13 ⋊ C2×C11⋊C5
HallC3×C11 ⋊ C5×D13
SylowC13 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C3×C5×D13

Subgroups

subgroupG/H
center, hypercenterC3D13×C11⋊C5
commutator, cosocle, hypocenterC11×C13C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C13C2×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 429

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(18,19,21,24,23)(20,22,26,27,25);(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(17,18,20,23,19,21,25,27,22,24,26)

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×D13×C11⋊C5, C11⋊C5×D13⋊C9, C3×C11⋊C5×D13⋊C3, …
maximal normal subgroup ofC9×D13×C11⋊C5, C11⋊C5×D13⋊C9, C3×C11⋊C5×D13⋊C3, …
maximal quotient ofC9×D13×C11⋊C5, C32×D13×C11⋊C5, C3×C11⋊C5×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 20);