Finite Group DatabasebetaFinite Group Databasebeta| order | 16121 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C47 · Schur multiplier (H2) = C72 |
| direct product | C47×H(3,𝔽7) |
| unambiguous semidirect product | C72⋊(C7×C47) |
| unambiguous semidirect product | (C72×C47)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C7×C47 | C72 |
| commutator, Frattini, cosocle | C7 | C72×C47 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C7×C47 ◁ G | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 2303 |
A minimal faithful permutation representation — 2 generators on 96 points:
(1,2,4,8,15,26,35)(3,6,10,17,28,37,44)(5,11,21,33,42,49,43)(7,13,20,30,39,36,45)(9,18,31,41,48,34,12)(14,24,19,32,27,38,46)(16,29,40,47,25,23,22)(50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96);(2,5,12,23,24,13,6)(4,9,19,10,11,22,20)(8,16,17,18,30,21,32)(15,27,33,39,31,28,29)(26,36,40,42,37,38,41)(35,44,45,46,47,48,49)2585 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16121, 3);