Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C2×C67×#1704 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C67 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C2×C42×C67 ◁ G | |
618 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 4 generators on 101 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(3,4,7,10)(5,11,13,18)(6,15,12,9)(8,16,17,14)(19,20)(21,27)(22,24)(23,31)(25,29)(26,30)(28,34)(32,33);(3,5,12,16,7,13,6,14)(4,8,15,18,10,17,9,11)(20,24)(25,33)(26,31)(27,34);(5,13)(8,17)(11,18)(14,16)(19,21,22,28)(20,25,24,33)(23,32,30,29)(26,34,31,27)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 12142);