Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C71 · Schur multiplier (H2) = C28 |
| direct product | C71×#62000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C71 |
| prime radical | C71×#3482 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C4×#41×C71 ◁ G | |
1818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 9088 |
A minimal faithful permutation representation — 5 generators on 95 points:
(2,5)(3,7)(9,10,13,17)(11,18,14,15)(12,20,21,24)(16,22,23,19)(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);(1,2)(3,6)(4,5)(7,8)(9,11,13,14)(10,15,17,18)(12,19,21,22)(16,20,23,24);(9,12)(10,16)(11,19)(13,21)(14,22)(15,20)(17,23)(18,24);(2,5)(6,8)(9,11,13,14)(10,15,17,18)(12,19,21,22)(16,20,23,24);(1,3,4,7)(2,6,5,8)(9,11,13,14)(10,15,17,18)(12,19,21,22)(16,20,23,24)3692 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 54988);