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C5×C11×D117 #27166018

order12870
isoclinismisoclinic class of D117
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D117
unambiguous semidirect productC9⋊(C5×C11×D13)
unambiguous semidirect productC13⋊(C5×C11×D9)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C2
derived, HallC9×C13 ⋊ C2×C5×C11
HallC9×C11×C13 ⋊ C2×C5
HallC5×C11×C13 ⋊ D9
HallC5×C9×C13 ⋊ C2×C11
HallC5×C9×C11 ⋊ D13
HallC11×C13 ⋊ C5×D9
HallC9×C11 ⋊ C5×D13
HallC5×C13 ⋊ C11×D9
HallC5×C9 ⋊ C11×D13
SylowC13 ⋊ C5×C11×D9
SylowC9 ⋊ C5×C11×D13

Subgroups

subgroupG/H
center, hypercenterC5×C11D117
commutator, cosocle, hypocenterC9×C13C2×C5×C11
FrattiniC3C5×C11×D39
FittingC5×C9×C11×C13C2
socleC3×C5×C11×C13D3
LCSG ▷ C9×C13
UCSC1 ◁ C5×C11

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

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×D9×D13, C5×D11×D117, C5×D99⋊D13, …
maximal normal subgroup ofC5×C11×D9×D13, C5×D11×D117, C5×D99⋊D13, …
maximal quotient ofC5×C11×Dic117, C2×C5×C11×D117

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 13);