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C9×C13×D55 #27166015

order12870
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×C13×D55
unambiguous semidirect productC5⋊(C9×C13×D11)
unambiguous semidirect productC11⋊(C9×D5×C13)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C2
derived, HallC5×C11 ⋊ C2×C9×C13
HallC9×C11×C13 ⋊ D5
HallC5×C11×C13 ⋊ C2×C9
HallC5×C9×C13 ⋊ D11
HallC5×C9×C11 ⋊ C2×C13
HallC11×C13 ⋊ C9×D5
HallC9×C11 ⋊ D5×C13
HallC5×C13 ⋊ C9×D11
HallC5×C9 ⋊ C13×D11
SylowC11 ⋊ C9×D5×C13
SylowC5 ⋊ C9×C13×D11

Subgroups

subgroupG/H
center, hypercenterC9×C13D55
commutator, hypocenterC5×C11C2×C9×C13
FrattiniC3C3×C13×D55
FittingC5×C9×C11×C13C2
socleC3×C5×C11×C13C2×C3
prime radicalC3×C13×D55C3
cosocleC3×C5×C11C2×C3×C13
LCSG ▷ C5×C11
UCSC1 ◁ C9×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:

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

Conjugacy classes & character table

3393 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×D13×D55, C9×D5×C13×D11, C9×D55⋊D13, …
maximal normal subgroup ofC9×D13×D55, C9×D5×C13×D11, C9×D55⋊D13, …
maximal quotient ofC9×C13×Dic55, C2×C9×C13×D55

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 10);