Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#11180 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C71 | #397 |
| commutator | C22×C4 | C22×C4×C71 |
| Frattini, cosocle | C23×C4 | C23×C71 |
| socle | C2×C71 | #1440 |
| prime radical | C22×#41×C71 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C71 ◁ C23×C4×C71 ◁ G | |
820 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 3 generators on 103 points:
(1,2)(3,12,16,8)(4,17,20,27)(5,11)(6,21)(7,10)(9,19,26,22)(13,25)(14,28,15,24)(18,23)(29,31)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3)(2,8)(4,18)(5,15)(6,14)(7,16)(9,25)(10,12)(11,28)(13,19)(17,29)(20,31)(21,24)(22,30)(23,27)(26,32);(1,4)(2,9,10,26)(3,13)(5,19)(6,22)(7,20)(8,23,12,29)(11,17,21,27)(14,18)(15,31)(16,30)(24,32,28,25)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4168);