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C9×D715 #27166016

order12870
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D715
unambiguous semidirect productC5⋊(C9×D143)
unambiguous semidirect productC11⋊(C9×D65)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C2
derived, HallC5×C11×C13 ⋊ C2×C9
HallC9×C11×C13 ⋊ D5
HallC5×C9×C13 ⋊ D11
HallC5×C9×C11 ⋊ D13
HallC11×C13 ⋊ C9×D5
HallC9×C13 ⋊ D55
HallC9×C11 ⋊ D65
HallC5×C13 ⋊ C9×D11
HallC5×C11 ⋊ C9×D13
HallC5×C9 ⋊ D143
SylowC13 ⋊ C9×D55
SylowC11 ⋊ C9×D65
SylowC5 ⋊ C9×D143

Subgroups

subgroupG/H
center, hypercenterC9D715
commutator, hypocenterC5×C11×C13C2×C9
FrattiniC3C3×D715
FittingC5×C9×C11×C13C2
socle, cosocleC3×C5×C11×C13C2×C3
prime radicalC3×D715C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ 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)(26,27)(28,29)(30,31,33,32,34,36,35,37,38);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,19,21,23,24,22,20,18,16)(25,26,28,29,27)

Conjugacy classes & character table

3231 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×D13×D55, C9×D11×D65, C9×D5×D143, …
maximal normal subgroup ofC9×D13×D55, C9×D11×D65, C9×D5×D143, …
maximal quotient ofC9×Dic715, C2×C9×D715

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 11);