Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#12945 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #447 |
| commutator | C2×C8 | C22×C4×C67 |
| Frattini, cosocle | C22×C8 | C23×C67 |
| prime radical | C2×#135×C67 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ #405×C67 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2,4,3)(5,6)(7,18)(8,12)(9,27)(10,28)(11,17)(13,20)(14,23)(15,26)(16,25)(19,32)(21,31)(22,34)(24,33)(29,30)(35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3,4,2)(6,12)(8,23)(9,26)(10,25)(13,30)(14,16)(15,17)(18,32)(19,20)(21,29)(24,36)(27,28)(31,33)(34,35);(5,7)(6,13)(8,24)(9,19)(10,29)(11,22)(12,30)(14,34)(15,31)(16,35)(17,33)(18,27)(20,26)(21,25)(23,36)(28,32)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 5933);