Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#24279 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C23×C4×C71 ◁ G | |
1328 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 107 points:
(5,6)(7,19)(8,23)(9,13)(10,17)(11,16)(12,18)(14,25)(15,22)(20,34)(21,29)(24,33)(26,32)(27,31)(28,35)(30,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,2)(3,4)(5,7,11,21,12,22,10,9)(6,13,17,15,18,29,16,19)(8,20,27,36,26,35,25,24)(14,28,32,30,31,34,23,33);(2,4)(5,8)(6,14)(7,20)(9,24)(10,25)(11,27)(12,26)(13,28)(15,30)(16,23)(17,32)(18,31)(19,33)(21,36)(22,35)(29,34);(5,9,10,22,12,21,11,7)(6,15,16,13,18,19,17,29)(8,24,25,35,26,36,27,20)(14,30,23,28,31,33,32,34)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 17267);