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C2×C3×C13×C11⋊C5 #16864237

order4290
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC2×C3×C11×C13 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C5×C13
HallC3×C11×C13 ⋊ C2×C5
HallC2×C11×C13 ⋊ C3×C5
HallC11×C13 ⋊ C2×C3×C5
HallC2×C3×C11 ⋊ C5×C13
HallC3×C11 ⋊ C2×C5×C13
HallC2×C11 ⋊ C3×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C11×C13C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 858

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C9×C13×C11⋊C5, C2×C11⋊C5×C13⋊C9, C2×C3×C13⋊C3×C11⋊C5, …
maximal normal subgroup ofC2×C9×C13×C11⋊C5, C2×C11⋊C5×C13⋊C9, C2×C3×C13⋊C3×C11⋊C5, …
maximal quotient ofC2×C9×C13×C11⋊C5, C3×D3×C13×C11⋊C5, C2×C32×C13×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 2);