Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C71 · Schur multiplier (H2) = C26 |
| direct product | C71×#24461 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C71 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C71 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C71 ◁ C22×C4×C71 ◁ G | |
1318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4544 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2,3,4)(5,6)(7,16)(8,22)(9,25)(10,14)(11,15)(12,19)(13,23)(17,21)(18,27)(20,28)(24,29)(26,30)(31,33)(32,35)(34,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(5,7,11,21)(6,12,15,28)(8,18,24,34)(9,20,10,19)(13,27,30,36)(14,17,25,16)(22,31,29,32)(23,35,26,33);(2,4)(5,6)(7,17)(8,13)(9,14)(10,25)(11,15)(12,19)(16,21)(18,32)(20,28)(22,23)(24,30)(26,29)(27,35)(31,34)(33,36);(5,8,11,24)(6,13,15,30)(7,18,21,34)(9,26,10,23)(12,27,28,36)(14,29,25,22)(16,31,17,32)(19,35,20,33)3053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 17449);