Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C71 · Schur multiplier (H2) = C2×C4 |
| direct product | C71×#12008 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C71 | D8 |
| commutator | C8 | C22×C8×C71 |
| Frattini, cosocle | C4×C8 | C23×C71 |
| socle | C22×C71 | C2×#107 |
| prime radical | C23×C71 | #107 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C71 ◁ C2×C42×C71 ◁ C2×C4×C8×C71 ◁ G | |
242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,2,3,5,4,6,7,8)(9,10)(11,20)(12,17)(13,27)(14,29)(15,19)(16,23)(18,21)(22,33)(24,39)(25,35)(26,32)(28,40)(30,37)(31,38)(34,36)(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);(9,11,21,36,14,24,28,38,15,25,26,37,12,22,13,23)(10,16,27,33,17,30,32,35,19,31,40,39,29,34,18,20);(9,12,15,14)(10,17,19,29)(11,22,25,24)(13,26,28,21)(16,30,31,34)(18,27,32,40)(20,33,35,39)(23,37,38,36)6248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4996);