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C3×C5×C13×D11 #16864241

order4290
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×D11

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C2
derived, SylowC11 ⋊ C2×C3×C5×C13
HallC5×C11×C13 ⋊ C2×C3
HallC3×C11×C13 ⋊ C2×C5
HallC3×C5×C11 ⋊ C2×C13
HallC11×C13 ⋊ C2×C3×C5
HallC5×C11 ⋊ C2×C3×C13
HallC3×C11 ⋊ C2×C5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13D11
commutator, cosocle, hypocenterC11C2×C3×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C2
LCSG ▷ C11
UCSC1 ◁ C3×C5×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 2145

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32);(23,32)(24,31)(25,30)(26,29)(27,28)

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×C13×D11, C5×D11×C13⋊C9, C3×C5×D11×C13⋊C3, …
maximal normal subgroup ofC5×C9×C13×D11, C5×D11×C13⋊C9, C3×C5×D11×C13⋊C3, …
maximal quotient ofC5×C9×C13×D11, C3×C5×C13×D33, C32×C5×C13×D11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 6);