Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#11130 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | #392 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| prime radical | C24×C71 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
862 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)(7,16)(8,13)(9,25)(10,14)(11,15)(12,18)(17,28)(19,33)(20,27)(21,36)(22,31)(23,29)(24,30)(26,34)(32,35)(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);(5,7,9,18,11,19,10,20)(6,12,14,16,15,27,25,33)(8,21,22,17,24,34,23,35)(13,28,29,36,30,32,31,26);(5,8,11,24)(6,13,15,30)(7,17,19,35)(9,23,10,22)(12,26,27,36)(14,31,25,29)(16,32,33,28)(18,21,20,34)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4118);