Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C27×C4 |
| direct product | C67×#36687 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C67 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C67 |
| socle | C23×C67 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C67 ◁ G | |
2446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 95 points:
(1,2,3,4)(5,6)(7,9)(8,10)(11,12)(13,14)(15,19)(16,20)(17,18)(21,24)(22,26)(23,25)(27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(5,7,8,12)(6,9,10,11)(14,18)(19,24)(20,25)(26,28);(2,4)(5,6)(7,11)(8,10)(9,12)(13,15)(14,19)(16,22)(17,21)(18,24)(20,26)(23,27)(25,28);(6,10)(9,11)(15,21)(19,24)(22,27)(26,28);(13,16,17,23)(14,20,18,25)(15,22,21,27)(19,26,24,28)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 29675);