Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#17391 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C71 |
| Frattini, cosocle | C22×C4 | C24×C71 |
| prime radical | C24×C71 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C2×C4×Q8×C71 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 119 points:
(1,2,4,7,5,8,11,14)(3,6,10,13,9,12,15,16)(17,18)(19,27,30,23)(20,24)(21,25)(22,26)(28,41,44,35)(29,42,46,36)(31,37)(32,38)(33,39)(34,40)(43,48,45,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(1,3)(2,6)(4,10)(5,9)(7,13)(8,12)(11,15)(14,16)(17,19,22,30)(18,23,26,27)(20,28,32,44)(21,29,34,46)(24,35,38,41)(25,36,40,42)(31,43,33,45)(37,47,39,48);(3,9)(6,12)(10,15)(13,16)(17,20,22,32)(18,24,26,38)(19,28,30,44)(21,33,34,31)(23,35,27,41)(25,39,40,37)(29,45,46,43)(36,48,42,47);(17,21,22,34)(18,25,26,40)(19,29,30,46)(20,31,32,33)(23,36,27,42)(24,37,38,39)(28,43,44,45)(35,47,41,48)4118 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 10379);