Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C24 |
| direct product | C71×#23681 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| socle | C23×C71 | C22×D4 |
| prime radical | C22×D4×C71 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ C43×C71 ◁ G | |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,3,4)(5,6)(7,10)(8,9)(11,12)(13,14)(15,18)(16,19)(17,20)(21,28)(22,26)(23,25)(24,27)(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);(6,9)(10,12)(13,15,16,22)(14,18,19,26)(17,21,24,23)(20,28,27,25);(2,4)(14,19)(15,21)(17,24)(18,25)(22,23)(26,28);(5,7,8,11)(6,10,9,12)4544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 16669);