Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C73 · Schur multiplier (H2) = C25 |
| direct product | C2×C73×#2220 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C73 |
| prime radical | C2×#466×C73 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C23×C4×C73 ◁ C23×C8×C73 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9344 |
A minimal faithful permutation representation — 4 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)(8,12)(9,16)(10,17)(13,18)(14,19)(15,22)(20,21);(7,8,13,22,10,15,9,12,11,14,16,21,17,20,18,19);(4,6)(8,14)(12,19)(15,20)(21,22)3796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 26591);