Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C71 · Schur multiplier (H2) = C23 |
| direct product | C71×#7884 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C71 | C2×D4 |
| commutator | C2×C4 | C2×C42×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| socle | C22×C71 | C2×#95 |
| prime radical | C24×C71 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C71 ◁ C22×C42×C71 ◁ G | |
572 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2)(3,9)(4,12)(5,8)(6,11)(7,13)(10,15)(14,16)(17,18,20,24,22,26,21,25)(19,23,28,31,27,30,29,32)(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)(2,6,8,14)(4,11)(5,10)(7,9,12,15)(13,16)(17,19,21,29,22,27,20,28)(18,23,25,32,26,30,24,31);(3,10)(6,14)(9,15)(11,16)(19,27)(23,30)(28,29)(31,32)5396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 872);