Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C71 · Schur multiplier (H2) = C23 |
| direct product | C71×#12869 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C71 | C2×D8 |
| commutator | C2×C8 | C22×C4×C71 |
| Frattini, cosocle | C22×C8 | C23×C71 |
| socle | C22×C71 | C2×#102 |
| prime radical | C24×C71 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C71 ◁ C23×C4×C71 ◁ C23×C8×C71 ◁ G | |
404 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,2)(3,6)(4,5)(7,8)(9,10,13,18,15,19,14,29)(11,20,22,36,23,37,30,34)(12,24,26,35,28,39,27,17)(16,25,31,38,33,40,32,21)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(2,5)(6,8);(1,3,4,7)(2,6,5,8)(9,11)(10,16)(12,25)(13,22)(14,30)(15,23)(17,34)(18,31)(19,33)(20,24)(21,27)(26,38)(28,40)(29,32)(35,36)(37,39)4118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 5857);