Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#11015 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #386 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| prime radical | C22×#41×C71 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
1242 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2)(3,4)(5,6,10,16,11,14,9,15)(7,17,20,27,21,12,19,28)(8,13,23,31,24,30,25,32)(18,33,22,36,34,26,35,29)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(5,7,11,21)(6,12,14,17)(8,22,24,35)(9,20,10,19)(13,29,30,36)(15,28,16,27)(18,25,34,23)(26,32,33,31);(2,4)(5,8)(6,13)(7,18)(9,25)(10,23)(11,24)(12,26)(14,30)(15,32)(16,31)(17,33)(19,35)(20,22)(21,34)(27,36)(28,29)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4003);