Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#17625 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C71 |
| Frattini, cosocle | C22×C4 | C24×C71 |
| prime radical | C71×#3505 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C4×D4×C71 ◁ G | |
1002 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,9,11,6)(4,12)(5,8)(7,13)(10,14,16,15)(17,18)(19,26)(20,25)(21,29)(22,24)(23,27)(28,32)(30,31)(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)(2,6)(4,10)(5,11)(7,14)(8,9)(12,15)(13,16)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(1,4)(2,7)(3,10)(5,13)(6,14)(8,12)(9,15)(11,16)(18,24)(23,31)(25,29)(26,32);(4,13)(7,12)(10,16)(14,15)(17,20,22,21)(18,25,24,29)(19,27,28,30)(23,32,31,26)3479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 10613);