Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#13032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C71 | #1879 |
| commutator | C2×C8 | C22×C4×C71 |
| Frattini, cosocle | C22×C8 | C23×C71 |
| prime radical | C2×#509×C71 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C71 ◁ C22×C4×C71 ◁ #405×C71 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2,7,13,15,18,6,11,9,14,24,17,8,3,5,12)(4,19,21,10,27,28,20,16,23,32,25,30,22,31,26,29)(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);(1,3,15,14,9,18,8,2)(4,16,22,30,23,29,27,10)(5,12,7,17,6,11,24,13)(19,21,28,26,32,25,31,20);(1,4)(2,10)(3,16)(5,21)(6,25)(7,26)(8,27)(9,23)(11,31)(12,28)(13,19)(14,30)(15,22)(17,32)(18,29)(20,24)2840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 6020);