Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C71 · Schur multiplier (H2) = C25 |
| direct product | C71×#17764 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C71 |
| Frattini, cosocle | C42 | C24×C71 |
| prime radical | C71×#3511 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C4×#41×C71 ◁ G | |
964 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2,5,7,6,3,4,8)(9,10,13,19,14,18,12,17)(11,16,20,24,21,15,22,23)(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);(1,3)(2,6)(4,8)(5,7)(9,11)(10,15)(12,20)(13,22)(14,21)(16,18)(17,23)(19,24);(1,4,6,5)(2,7,3,8)(9,11)(10,16)(12,22)(13,20)(14,21)(15,18)(17,23)(19,24);(9,12,14,13)(10,17,18,19)(11,20,21,22)(15,23,16,24)3479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 10752);