Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#17718 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | C2×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C71 |
| Frattini, cosocle | C42 | C24×C71 |
| socle | C22×C71 | C22×C22⋊C4 |
| prime radical | C24×C71 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C22×C42×C71 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,5,10,6,8,4,9)(3,11,12,16,13,7,14,15)(17,18)(19,25)(20,28)(21,23)(22,26)(24,30)(27,32)(29,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3,6,13)(2,7,8,11)(4,12,5,14)(9,15,10,16)(17,19,21,27)(18,22,23,31)(20,29,30,26)(24,32,28,25);(2,8)(7,11)(9,10)(15,16)(18,23)(22,31)(24,28)(25,32);(1,4,6,5)(2,9,8,10)(3,12,13,14)(7,15,11,16)4544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 10706);