Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C73×#60433 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C73 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C4×#41×C73 ◁ G | |
2678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 4672 |
A minimal faithful permutation representation — 5 generators on 109 points:
(2,4)(5,6)(7,15)(8,13)(9,11)(10,22)(12,18)(14,21)(16,29)(17,28)(19,25)(20,33)(23,24)(26,31)(27,32)(30,36)(34,35)(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);(1,2,3,4)(6,11)(12,24)(13,25)(14,22)(15,28)(26,35)(27,33)(29,36);(5,7,9,17)(6,12,11,24)(8,16,19,30)(10,23,21,18)(13,26,25,35)(14,28,22,15)(20,34,32,31)(27,36,33,29);(5,8)(6,13)(7,16)(9,19)(10,20)(11,25)(12,26)(14,27)(15,29)(17,30)(18,31)(21,32)(22,33)(23,34)(24,35)(28,36);(8,19)(13,25)(16,30)(20,32)(26,35)(27,33)(29,36)(31,34)4453 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53421);