Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#10791 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C2×D4 |
| commutator | C2×C4 | C2×C42×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| socle | C23×C71 | C4×D4 |
| prime radical | C22×#41×C71 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ C23×C8×C71 ◁ G | |
1250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2)(3,4)(5,6,7,8)(9,10)(11,13)(12,20)(14,17)(15,18)(16,22)(19,23)(21,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(2,4)(9,11,13,18,15,17,14,10)(12,19,22,24,23,20,21,16);(9,12)(10,16)(11,19)(13,22)(14,21)(15,23)(17,20)(18,24)5396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 3779);