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×#61088 |
| 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 ◁ #532×C67 ◁ G | |
2714 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)(5,6,11,16)(7,17,21,34)(8,13,24,32)(9,15,10,14)(12,26,29,20)(18,28,22,36)(19,27,35,30)(23,33,25,31)(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)(6,12)(8,22)(9,20)(10,26)(11,21)(13,30)(14,17)(15,34)(16,29)(18,24)(19,23)(25,35)(27,32)(28,31)(33,36);(2,4)(5,8)(6,13)(7,18)(9,25)(10,23)(11,24)(12,27)(14,33)(15,31)(16,32)(17,28)(19,20)(21,22)(26,35)(29,30)(34,36);(5,8)(6,13)(7,19)(9,23)(10,25)(11,24)(12,28)(14,31)(15,33)(16,32)(17,27)(18,20)(21,35)(22,26)(29,36)(30,34);(5,9,11,10)(6,14,16,15)(7,20,21,26)(8,23,24,25)(12,17,29,34)(13,31,32,33)(18,35,22,19)(27,36,30,28)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54076);