Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C2×C73×#3063 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| prime radical | C2×#537×C73 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C22×#41×C73 ◁ G | |
2742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 5 generators on 95 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(3,4)(5,6)(7,8,12,16)(9,17,19,20)(10,14,13,22)(11,18,21,15);(7,9,11,14,12,19,21,22)(8,13,15,17,16,10,18,20);(4,6)(7,10)(8,14)(9,18)(11,20)(12,13)(15,19)(16,22)(17,21);(9,19)(10,13)(14,22)(17,20)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53440);