Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C71 · Schur multiplier (H2) = C22 |
| direct product | C71×#7181 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C71 | #102 |
| commutator | C8 | C4×C8×C71 |
| Frattini, cosocle | C2×C4×C8 | C22×C71 |
| socle | C2×C71 | #1279 |
| prime radical | C23×C71 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C71 ◁ C22×C8×C71 ◁ C2×C4×C8×C71 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 2272 |
A minimal faithful permutation representation — 2 generators on 103 points:
(1,2,5,10,7,12,23,28,8,13,22,29,6,11,4,20)(3,14,16,25,18,31,15,9,19,24,32,26,17,30,21,27)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3,6,17,8,19,7,18)(2,9)(4,21,22,32,23,15,5,16)(10,24)(11,25)(12,26)(13,27)(14,29)(20,31)(28,30)4544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 169);