Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#24280 |
| 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)(7,15)(8,22)(9,26)(10,17)(11,16)(12,18)(13,20)(14,24)(19,33)(21,29)(23,36)(25,32)(27,31)(28,35)(30,34)(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)(5,7,10,20,12,21,11,9)(6,13,16,15,18,26,17,29)(8,19,24,34,25,35,27,23)(14,28,22,30,31,33,32,36);(2,4)(5,8)(6,14)(7,19)(9,23)(10,24)(11,27)(12,25)(13,28)(15,30)(16,22)(17,32)(18,31)(20,34)(21,35)(26,33)(29,36);(5,9,11,21,12,20,10,7)(6,15,17,13,18,29,16,26)(8,23,27,35,25,34,24,19)(14,30,32,28,31,36,22,33)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 17268);