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C9×C11⋊(C13⋊D13) #45689554

order33462
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C13

Aliases

direct productC9×C11⋊(C13⋊D13)
unambiguous semidirect productC11⋊(C9×C13⋊D13)

Splittings

Fitting, HallC9×C11×C132 ⋊ C2
derived, HallC11×C132 ⋊ C2×C9
HallC9×C132 ⋊ D11
SylowC132 ⋊ C9×D11
HallC9×C11 ⋊ C13⋊D13
SylowC11 ⋊ C9×C13⋊D13

Subgroups

subgroupG/H
center, hypercenterC9C11⋊(C13⋊D13)
commutator, hypocenterC11×C132C2×C9
FrattiniC3C3×C11⋊(C13⋊D13)
FittingC9×C11×C132C2
socle, cosocleC3×C11×C132C2×C3
prime radicalC3×C11⋊(C13⋊D13)C3
LCSG ▷ C11×C132
UCSC1 ◁ C9

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 16731

A minimal faithful permutation representation — 3 generators on 46 points:

(1,2,3,4,5,6,7,8,9)(11,12)(13,14)(15,16)(17,18)(19,20)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46);(10,11,13,15,17,19,20,18,16,14,12)(34,35,37,39,41,43,45,46,44,42,40,38,36);(21,22,24,26,28,30,32,33,31,29,27,25,23)

Conjugacy classes & character table

8379 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33462, 62);