Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#9929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C73 |
| prime radical | C24×C73 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C23×C4×C73 ◁ G | |
610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 3 generators on 109 points:
(1,2)(3,4)(5,6,10,13)(7,14,16,19)(8,12,9,17)(11,18,20,15)(21,22)(23,26)(24,27)(25,28)(29,32)(30,33)(31,35)(34,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(5,7,10,16)(6,11,13,20)(8,15,9,18)(12,19,17,14)(21,23,25,30)(22,26,28,33)(24,29,31,36)(27,34,35,32);(2,4)(5,8,10,9)(6,12,13,17)(7,15,16,18)(11,19,20,14)(21,24)(22,27)(23,29)(25,31)(26,32)(28,35)(30,36)(33,34)2920 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 2917);