Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C27 |
| direct product | C67×#23893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
1610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 131 points:
(1,2)(3,14)(4,20)(5,26)(6,30)(7,12)(8,13)(9,17)(10,24)(11,27)(15,43)(16,32)(18,34)(19,33)(21,41)(22,52)(23,38)(25,37)(28,40)(29,39)(31,45)(35,49)(36,55)(42,46)(44,61)(47,58)(48,57)(50,53)(51,56)(54,60)(59,64)(62,63)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(1,3)(2,9)(4,21)(5,16)(6,18)(7,17)(8,19)(10,35)(11,32)(12,33)(13,34)(14,30)(15,23)(20,31)(22,51)(24,45)(25,49)(26,42)(27,48)(28,46)(29,47)(36,59)(37,43)(38,41)(39,57)(40,58)(44,54)(50,56)(52,61)(53,64)(55,63)(60,62);(1,4)(2,10)(3,15)(5,22)(6,23)(7,24)(8,25)(9,31)(11,36)(12,37)(13,38)(14,41)(16,44)(17,21)(18,49)(19,45)(20,30)(26,50)(27,53)(28,54)(29,55)(32,56)(33,35)(34,43)(39,60)(40,52)(42,61)(46,63)(47,64)(48,51)(57,59)(58,62);(1,5,8,29)(2,11,13,40)(3,16,19,47)(4,22,25,55)(6,28,7,27)(9,32,34,58)(10,36,38,52)(12,39,30,26)(14,42,33,57)(15,44,45,64)(17,48,18,46)(20,50,37,60)(21,51,49,63)(23,54,24,53)(31,56,43,62)(35,59,41,61)2680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 16881);