Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#33671 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| prime radical | C67×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ C2×C4×C8×C67 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,21)(12,18)(13,19)(14,17)(15,29)(16,23)(20,28)(22,36)(24,35)(25,31)(26,33)(27,34)(30,39)(32,38)(37,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,5)(6,8)(9,11,13,23)(10,16,19,21)(12,22,15,25)(14,24,27,39)(17,30,34,35)(18,31,29,36)(20,32,33,37)(26,38,28,40);(10,17)(12,15)(14,28)(16,30)(18,20)(19,34)(21,35)(22,25)(24,40)(26,27)(29,33)(31,32)(36,37)(38,39);(1,3,4,7)(2,6,5,8)(9,12,13,15)(10,18,19,29)(11,22,23,25)(14,26,27,28)(16,31,21,36)(17,33,34,20)(24,38,39,40)(30,37,35,32)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26659);