Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C71 · Schur multiplier (H2) = C23 |
| direct product | C2×C71×#1313 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C71 | C42 |
| commutator | C4 | C2×C4×C8×C71 |
| Frattini, cosocle | C4×C8 | C23×C71 |
| socle, prime radical | C23×C71 | #97 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C71 ◁ G | |
302 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 18176 |
A minimal faithful permutation representation — 3 generators on 97 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(11,12,13,17,14,19,21,25,15,18,20,26,22,16,23,24);(3,4,5,7,6,8,9,10)(12,16,18,19)(13,20)(17,25,26,24)(21,23)6248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 4391);