Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C71 · Schur multiplier (H2) = C42 |
| direct product | C71×#8138 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C71 | C42 |
| commutator | C4 | C2×C4×C8×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| socle | C22×C71 | #376 |
| prime radical | C23×C71 | #117 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C71 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,2,4,6,3,5,7,8)(9,10)(11,19,22,32)(12,16)(13,17)(14,18)(15,21,27,35)(20,31,34,39)(23,28)(24,29)(25,30)(26,33,37,40)(36,38)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(2,5)(6,8)(9,11)(10,15,18,27)(12,20)(13,21)(14,22)(16,26,29,37)(17,19,30,32)(23,33)(24,34)(25,35)(28,31,38,39)(36,40);(9,12,13,23,14,24,25,36)(10,16,17,28,18,29,30,38)(11,20,21,33,22,34,35,40)(15,26,19,31,27,37,32,39)6248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 1126);