Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C71 · Schur multiplier (H2) = C22×C4 |
| direct product | C71×#9656 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C2×D4 |
| commutator | C2×C4 | C22×C8×C71 |
| Frattini, cosocle | C2×C42 | C23×C71 |
| socle, prime radical | C23×C71 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ C2×C4×C8×C71 ◁ G | |
502 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 18176 |
A minimal faithful permutation representation — 3 generators on 99 points:
(2,4)(5,6,8,11,9,7,10,12)(13,14)(15,20)(16,25)(17,27)(18,22)(19,23)(21,26)(24,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,2,3,4)(5,7,8,12,9,6,10,11)(13,15,17,23,18,24,26,16)(14,19,21,20,22,25,27,28);(13,16,26,24,18,23,17,15)(14,20,27,19,22,28,21,25)6248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 2644);