Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C22×C4 |
| direct product | C67×#9742 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C67 | #121 |
| commutator | C42 | C22×C4×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C2×C42×C67 ◁ G | |
506 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,4)(5,6,7,10,8,11,12,9)(13,14)(15,23)(16,19)(17,26)(18,22)(20,24)(21,27)(25,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(1,2,3,4)(6,9)(7,12)(10,11)(13,15,17,16,18,24,27,25)(14,19,21,23,22,28,26,20);(13,16,17,24,18,25,27,15)(14,20,21,19,22,23,26,28)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 2730);