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×#33557 |
| 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 | |
1258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1072 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2)(3,7)(4,8)(5,9)(6,11)(10,15)(12,14)(13,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(1,3)(2,6)(4,11)(5,10)(7,8)(9,14)(12,13)(15,16);(1,3)(2,7)(4,12)(5,10)(6,8)(9,15)(11,13)(14,16);(3,10)(6,14)(7,15)(11,12)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26545);