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C9×D5×C11×C13 #27166013

order12870
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C9×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×D5×C11×C13
unambiguous semidirect productC5⋊(C2×C9×C11×C13)

Splittings

Fitting, HallC5×C9×C11×C13 ⋊ C2
derived, SylowC5 ⋊ C2×C9×C11×C13
HallC5×C11×C13 ⋊ C2×C9
HallC5×C9×C13 ⋊ C2×C11
HallC5×C9×C11 ⋊ C2×C13
HallC5×C13 ⋊ C2×C9×C11
HallC5×C11 ⋊ C2×C9×C13
HallC5×C9 ⋊ C2×C11×C13

Subgroups

subgroupG/H
center, hypercenterC9×C11×C13D5
commutator, hypocenterC5C2×C9×C11×C13
FrattiniC3C3×D5×C11×C13
FittingC5×C9×C11×C13C2
socleC3×C5×C11×C13C2×C3
prime radicalC3×D5×C11×C13C3
cosocleC3×C5C2×C3×C11×C13
LCSG ▷ C5
UCSC1 ◁ C9×C11×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)(6,7,8,9,10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29)(30,31,33,32,34,36,35,37,38);(1,2,4,5,3)

Conjugacy classes & character table

5148 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C11×C13×AGL(1,𝔽5), C9×C11×#63120, C9×C13×C11⋊AGL(1,𝔽5), …
maximal normal subgroup ofC9×C11×C13×AGL(1,𝔽5), C9×C11×#63120, C9×C13×C11⋊AGL(1,𝔽5), …
maximal quotient ofC9×C11×C13×Dic5, C2×C9×D5×C11×C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12870, 8);