Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C113 · Schur multiplier (H2) = C25 |
| direct product | C113×#25157 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C113 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C113 |
| prime radical | C2×#121×C113 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G | |
1100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 14464 |
A minimal faithful permutation representation — 4 generators on 137 points:
(5,6,8,7)(9,10,13,17)(11,18,20,24)(12,14,21,16)(15,22,23,19)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,2)(3,4)(5,7,8,6)(10,14)(12,21)(15,18)(16,17)(19,22)(23,24);(2,4)(6,7);(9,11,13,20)(10,15,17,23)(12,22,21,19)(14,18,16,24)5876 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 18145);