Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C2×C67×#3162 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C23×C67 | C22×D4 |
| prime radical | C24×C67 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ C22×C42×C67 ◁ G | |
1902 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(3,4,6,8)(5,9,10,7)(11,12)(13,20)(14,18)(15,24)(16,19)(17,23)(21,26)(22,25);(3,5,6,10)(4,7,8,9)(13,21)(17,25)(20,26)(22,23);(11,13,15,23,16,21,14,22)(12,17,18,20,19,25,24,26);(11,14,16,15)(12,18,19,24)(13,22,21,23)(17,20,25,26)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53645);