Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#11013 |
| 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 | |
1262 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)(7,15,18,11)(8,12)(9,14)(10,13)(16,33,34,25)(17,31,22,26)(19,36,35,27)(20,29)(21,28)(23,32)(24,30)(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)(6,11)(8,19)(9,22)(10,18)(12,27)(13,15)(14,31)(16,20)(17,24)(21,35)(23,34)(25,29)(26,30)(28,36)(32,33);(2,4)(5,8,10,21)(6,12,13,28)(7,16,18,34)(9,23,24,20)(11,25,15,33)(14,32,30,29)(17,35,22,19)(26,36,31,27)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4001);