Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C26 |
| direct product | C67×#33556 |
| 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 ◁ C2×C4×C67 ◁ C2×#41×C67 ◁ G | |
1134 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)(3,13)(4,9)(5,10)(6,11)(7,12)(8,15)(14,27)(16,28)(17,23)(18,32)(19,25)(20,26)(21,29)(22,31)(24,30)(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);(1,3,7,16)(2,8,12,22)(4,14,5,18)(6,15,20,31)(9,21,10,24)(11,13,26,28)(17,29,19,30)(23,27,25,32);(1,4,7,5)(2,9,12,10)(3,14,16,18)(6,19,20,17)(8,21,22,24)(11,23,26,25)(13,27,28,32)(15,30,31,29);(1,5,7,4)(2,10,12,9)(3,14,16,18)(6,19,20,17)(8,21,22,24)(11,25,26,23)(13,27,28,32)(15,29,31,30)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26544);