Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C28 |
| direct product | C73×#60859 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C73 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| socle | C22×C73 | C23×D4 |
| prime radical | C73×#3455 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C73 ◁ C2×#117×C73 ◁ G | |
1654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 5 generators on 121 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18)(19,24)(20,32)(21,26)(22,35)(23,27)(25,33)(28,42)(29,38)(30,39)(31,45)(34,40)(36,41)(37,44)(43,48)(46,47)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19)(18,24)(20,28)(21,30)(22,31)(23,29)(25,37)(26,39)(27,38)(32,42)(33,44)(34,43)(35,45)(36,46)(40,48)(41,47);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,20)(18,25)(19,28)(21,33)(22,36)(23,34)(24,37)(26,40)(27,41)(29,43)(30,44)(31,46)(32,35)(38,47)(39,48)(42,45);(2,8)(6,9)(7,16)(14,15)(19,29)(24,38)(28,43)(30,31)(37,47)(39,45)(42,48)(44,46);(17,21,23,22)(18,26,27,35)(19,30,29,31)(20,33,34,36)(24,39,38,45)(25,40,41,32)(28,44,43,46)(37,48,47,42)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53847);