Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#19029 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | #121×C71 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,6,4)(3,9,11,16)(5,13,15,8)(7,14,10,12)(19,25)(20,27)(22,30)(23,28)(26,29)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3,6,11)(2,7,4,10)(5,14,15,12)(8,16,13,9)(17,18,21,24)(19,22,26,31)(20,28,27,23)(25,32,29,30);(1,4,6,2)(3,10,11,7)(5,8,15,13)(9,14,16,12)(17,19)(18,22)(20,29)(21,26)(23,32)(24,31)(25,27)(28,30);(3,11)(7,10)(9,16)(12,14)2627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 12017);