Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#61105 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C2×C67 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C22×C4×C67 ◁ G | |
2620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 5 generators on 99 points:
(1,2)(3,13)(4,15)(5,10)(6,11)(7,24)(8,12)(9,18)(14,30)(16,19)(17,31)(20,32)(21,27)(22,28)(23,29)(25,26)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3)(2,4)(5,20)(6,15)(7,16)(8,9)(10,26)(11,18)(12,19)(13,24)(14,21)(17,28)(22,25)(23,31)(27,32)(29,30);(1,4)(2,9)(3,12)(5,17)(6,18)(7,13)(8,19)(10,25)(11,16)(14,29)(15,24)(20,27)(21,26)(22,30)(23,32)(28,31);(1,5)(2,10)(3,14)(4,17)(6,21)(7,22)(8,23)(9,25)(11,27)(12,29)(13,30)(15,31)(16,20)(18,26)(19,32)(24,28);(1,6,8,7)(2,11,12,24)(3,15,9,16)(4,18,19,13)(5,21,23,22)(10,27,29,28)(14,31,25,20)(17,26,32,30)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54093);