Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#18617 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C71 |
| prime radical | C71×#3506 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C42×C71 ◁ G | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2,6,9)(3,10,13,15)(4,8,5,14)(7,12,16,11)(17,18,22,26)(19,27,28,31)(20,25,21,24)(23,30,32,29)(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);(1,3,6,13)(2,7,9,16)(4,11,5,12)(8,15,14,10)(17,19,22,28)(18,23,26,32)(20,30,21,29)(24,31,25,27);(1,4,6,5)(2,8,9,14)(3,11,13,12)(7,15,16,10)(18,24)(20,21)(23,31)(25,26)(27,32)(29,30);(1,4,6,5)(2,8,9,14)(3,12,13,11)(7,10,16,15)(19,28)(23,32)(27,31)(29,30)2840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 11605);