Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#61054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #525×C67 ◁ G | |
2710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2)(3,4)(5,6)(7,16)(8,13)(9,14)(10,23)(11,15)(12,17)(18,33)(19,26)(20,29)(21,36)(22,31)(24,28)(25,32)(27,34)(30,35)(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);(5,7,11,19)(6,12,15,28)(8,17,10,24)(9,21,22,34)(13,26,23,16)(14,30,31,33)(18,25,35,20)(27,29,36,32);(2,4)(5,8,11,10)(6,13,15,23)(7,17,19,24)(9,20,22,25)(12,26,28,16)(14,29,31,32)(18,34,35,21)(27,30,36,33);(5,9,11,22)(6,14,15,31)(7,18,19,35)(8,20,10,25)(12,27,28,36)(13,29,23,32)(16,33,26,30)(17,34,24,21);(6,15)(12,28)(13,23)(14,31)(16,26)(27,36)(29,32)(30,33)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54042);