Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#11186 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C71 | #394 |
| 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)(3,13,17,8)(4,18)(5,12)(6,11)(7,10)(9,20)(14,30,31,26)(15,24,16,25)(19,29,32,23)(21,28)(22,27)(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)(4,19)(5,16)(6,15)(7,17)(9,26)(10,13)(11,25)(12,24)(14,20)(18,23)(21,32)(22,31)(27,30)(28,29);(1,4)(2,9,10,27)(3,14)(5,20)(6,22)(7,21)(8,23,13,29)(11,18,12,28)(15,19)(16,32)(17,31)(24,26,25,30)3266 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4174);