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C5×C9×D143 #27166012

order12870
isoclinismisoclinic class of D143
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D143

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C2
derived, HallC11×C13 ⋊ C2×C5×C9
HallC9×C11×C13 ⋊ C2×C5
HallC5×C11×C13 ⋊ C2×C9
HallC5×C9×C13 ⋊ D11
HallC5×C9×C11 ⋊ D13
HallC9×C13 ⋊ C5×D11
HallC9×C11 ⋊ C5×D13
HallC5×C13 ⋊ C9×D11
HallC5×C11 ⋊ C9×D13
SylowC13 ⋊ C5×C9×D11
SylowC11 ⋊ C5×C9×D13

Subgroups

subgroupG/H
center, hypercenterC5×C9D143
commutator, hypocenterC11×C13C2×C5×C9
FrattiniC3C3×C5×D143
FittingC5×C9×C11×C13C2
socleC3×C5×C11×C13C2×C3
prime radicalC3×C5×D143C3
cosocleC3×C11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C5×C9

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:

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

Conjugacy classes & character table

3285 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×D11×D13, C9×D5×D143, C9×D55⋊D13, …
maximal normal subgroup ofC5×C9×D11×D13, C9×D5×D143, C9×D55⋊D13, …
maximal quotient ofC5×C9×Dic143, C2×C5×C9×D143

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 7);