Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12711 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#12713 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #1781 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C2×#41 | C23×C67 |
| prime radical | C67×#3485 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C2×C4×C67 ◁ C2×H(5,𝔽2)×C67 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2)(3,12)(4,16,18,9)(5,10)(6,11)(7,13,23,28)(8,17,24,19)(14,21)(15,26)(20,25)(22,27,32,29)(30,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3,6,15)(2,7,11,23)(4,13,18,28)(5,14,20,30)(8,21,24,31)(9,12,16,26)(10,22,25,32)(17,27,19,29);(1,4)(2,8)(3,13)(5,19)(6,18)(7,21)(9,10)(11,24)(12,22)(14,29)(15,28)(16,25)(17,20)(23,31)(26,32)(27,30)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 5701);