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C5×C9×C11×D13 #27166010

order12870
isoclinismisoclinic class of D13
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×C11×D13

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C9×C11D13
commutator, hypocenterC13C2×C5×C9×C11
FrattiniC3C3×C5×C11×D13
FittingC5×C9×C11×C13C2
socleC3×C5×C11×C13C2×C3
prime radicalC3×C5×C11×D13C3
cosocleC3×C13C2×C3×C5×C11
LCSG ▷ C13
UCSC1 ◁ C5×C9×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)(14,15,16,17,18,19,20,21,22,23,24)(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)

Conjugacy classes & character table

3960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×C11×#261, C5×C9×C11⋊#261, C5×C9×D11×D13, …
maximal normal subgroup ofC5×C9×C11×#261, C5×C9×C11⋊#261, C5×C9×D11×D13, …
maximal quotient ofC5×C9×C11×Dic13, C2×C5×C9×C11×D13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 5);