Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#9043 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | #120 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| prime radical | C2×#121×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C23×C4×C67 ◁ G | |
678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,4)(5,6,7,11,9,12,8,10)(13,14,17,21,18,22,16,20)(15,23,25,19,26,27,24,28)(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)(6,10)(7,8)(11,12)(13,15)(14,19)(16,25)(17,24)(18,26)(20,27)(21,23)(22,28);(6,11)(7,8)(10,12)(13,15)(14,19)(16,24)(17,25)(18,26)(20,23)(21,27)(22,28)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 2031);