Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C73 · Schur multiplier (H2) = C29 |
| direct product | C2×C73×#3045 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C73 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C73 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G | |
2934 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 4672 |
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);(4,6)(7,8)(9,13)(10,15)(11,20)(12,16)(14,17)(18,22)(19,21);(3,4,5,6)(7,9)(8,13)(10,19)(11,17)(12,18)(14,20)(15,21)(16,22);(7,9)(8,14)(10,17)(11,19)(12,18)(13,20)(15,22)(16,21);(7,10,12,11)(8,15,16,20)(9,17,18,19)(13,14,22,21)4672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 53408);