Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#18121 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| socle | C22×C71 | C2×#120 |
| prime radical | C71×#3460 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C23×C4×C71 ◁ G | |
990 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)(3,10)(4,8)(5,13)(6,9)(7,11)(12,15)(14,16)(17,18,21,24)(19,22,26,29)(20,23,27,30)(25,31,32,28)(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)(2,7)(4,11)(5,14)(6,12)(8,15)(9,16)(10,13)(17,19)(18,22)(20,25)(21,26)(23,28)(24,29)(27,32)(30,31);(17,20,21,27)(18,23,24,30)(19,25,26,32)(22,28,29,31);(1,4,6,5)(2,8,9,13)(3,11,12,14)(7,15,16,10)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 11109);