Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C71 · Schur multiplier (H2) = C2×C4 |
| direct product | C71×#11405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C71 | C42 |
| commutator | C4 | C2×C4×C8×C71 |
| Frattini, cosocle | C4×C8 | C23×C71 |
| socle | C22×C71 | C2×#97 |
| prime radical | C23×C71 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C71 ◁ G | |
282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 3 generators on 111 points:
(9,10,12,16,13,18,24,32,14,17,25,31,26,33,39,40)(11,19,21,35,22,28,37,30,20,34,23,38,36,15,27,29)(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);(1,2,3,5,4,6,7,8)(9,11)(10,15,17,28)(12,23)(13,22)(14,20)(16,30,31,29)(18,19,33,34)(21,25)(24,27)(26,36)(32,38,40,35)(37,39);(11,20)(15,28)(19,34)(21,23)(22,36)(27,37)(29,30)(35,38)6248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4393);