Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24×C4 |
| direct product | C67×#22277 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ #376×C67 ◁ G | |
826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 17152 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,4,3)(5,6)(7,10)(8,11)(9,12)(13,14)(15,23)(16,27)(17,21)(18,32)(19,25)(20,30)(22,31)(24,38)(26,34)(28,42)(29,41)(33,43)(35,39)(36,44)(37,40)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(1,3,4,2)(5,7,10,6)(8,11,9,12)(13,15)(14,19)(16,28)(17,25)(18,26)(20,35)(21,23)(22,34)(24,29)(27,38)(30,43)(31,40)(32,37)(33,36)(39,44)(41,42);(5,8,10,9)(6,11,7,12)(13,16,18,30,17,29,31,44)(14,20,22,27,21,36,32,41)(15,24,26,39,25,28,40,43)(19,33,34,42,23,35,37,38);(5,9,10,8)(6,11,7,12)(14,21)(15,25)(20,36)(22,32)(24,28)(26,40)(27,41)(39,43)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 15265);