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C5×C11×C13×D9 #27166017

order12870
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C13×D9
unambiguous semidirect productC9⋊(C2×C5×C11×C13)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C2
derived, SylowC9 ⋊ C2×C5×C11×C13
HallC9×C11×C13 ⋊ C2×C5
HallC5×C9×C13 ⋊ C2×C11
HallC5×C9×C11 ⋊ C2×C13
HallC9×C13 ⋊ C2×C5×C11
HallC9×C11 ⋊ C2×C5×C13
HallC5×C9 ⋊ C2×C11×C13

Subgroups

subgroupG/H
center, hypercenterC5×C11×C13D9
commutator, cosocle, hypocenterC9C2×C5×C11×C13
FrattiniC3C5×D3×C11×C13
FittingC5×C9×C11×C13C2
socleC3×C5×C11×C13D3
LCSG ▷ C9
UCSC1 ◁ C5×C11×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 6435

A minimal faithful permutation representation — 2 generators on 38 points:

(2,4)(3,7)(5,8)(6,9)(10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33)(34,35,36,37,38);(1,6,4,3,8,5,7,2,9)

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×D9×D13, C5×C13×D9×D11, C5×D9×D143, …
maximal normal subgroup ofC5×C11×D9×D13, C5×C13×D9×D11, C5×D9×D143, …
maximal quotient ofC5×C11×C13×Dic9, C2×C5×C11×C13×D9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 12);