Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#17991 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C42 | C24×C67 |
| socle | C22×C67 | C2×C4×D4 |
| prime radical | C23×C67 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ #431×C67 ◁ G | |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,5,9,6,8,14,15)(3,7,11,4,10,12,16,13)(17,18)(19,27)(20,24)(21,33)(22,25)(23,29)(26,35)(28,41)(30,40)(31,39)(32,45)(34,37)(36,43)(38,44)(42,48)(46,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3)(2,7)(4,9)(5,11)(6,10)(8,12)(13,15)(14,16)(17,19,22,30)(18,23,25,37)(20,28,31,42)(21,34,35,29)(24,36,39,47)(26,40,33,27)(32,46,44,43)(38,48,45,41);(1,4,5,12,6,13,14,7)(2,3,9,11,8,10,15,16)(17,20,22,31)(18,24,25,39)(19,28,30,42)(21,32,35,44)(23,36,37,47)(26,38,33,45)(27,41,40,48)(29,43,34,46);(2,8)(3,10)(9,15)(11,16)(18,25)(20,31)(23,37)(26,33)(27,40)(28,42)(32,44)(43,46)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 10979);