Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C26 |
| direct product | C67×#33558 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C67 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C23×C67 ◁ C22×D4×C67 ◁ G | |
1158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,11)(4,8)(5,9)(6,10)(7,14)(12,24)(13,25)(15,21)(16,22)(17,30)(18,23)(19,26)(20,28)(27,32)(29,31)(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);(1,3,6,13)(2,7,10,20)(4,12,15,27)(5,14,18,28)(8,19,21,31)(9,11,23,25)(16,26,17,29)(22,24,30,32);(1,4)(2,8)(3,12)(5,17)(6,15)(7,19)(9,22)(10,21)(11,24)(13,27)(14,29)(16,18)(20,31)(23,30)(25,32)(26,28);(3,13)(4,15)(7,20)(8,21)(11,25)(14,28)(16,17)(22,30)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26546);