Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C73 · Schur multiplier (H2) = C23 |
| direct product | C73×#10077 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C73 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G | |
550 conjugacy classes of subgroups.
| minimal degree | μ(G) = 101 |
| transitive degree | μt(G) = 18688 |
A minimal faithful permutation representation — 3 generators on 101 points:
(6,10)(7,11)(8,12)(13,14,18,21)(15,22,24,27)(16,20,17,25)(19,26,28,23)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,2)(3,4)(5,6)(7,9)(8,11)(10,12)(13,15,18,24)(14,19,21,28)(16,23,17,26)(20,27,25,22);(2,4)(5,7,9,6)(8,10,12,11)(13,16,18,17)(14,20,21,25)(15,23,24,26)(19,27,28,22)3358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 3065);