Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C113 · Schur multiplier (H2) = C24×C4 |
| direct product | C113×#18359 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C113 |
| prime radical | C113×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G | |
1004 conjugacy classes of subgroups.
| minimal degree | μ(G) = 145 |
| transitive degree | μt(G) = 3616 |
A minimal faithful permutation representation — 4 generators on 145 points:
(2,7)(3,11)(4,16)(8,21)(9,19)(10,17)(12,27)(14,30)(15,26)(18,29)(20,23)(22,32)(24,28)(25,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(1,2,5,10)(3,12,15,8)(4,17,16,7)(6,9,13,22)(11,24,26,23)(14,20,31,28)(18,32,29,19)(21,30,27,25);(4,18)(7,19)(14,25)(16,29)(17,32)(20,21)(27,28)(30,31);(1,3,13,26)(2,8,22,24)(4,14,29,30)(5,15,6,11)(7,20,32,27)(9,23,10,12)(16,31,18,25)(17,28,19,21)3842 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 11347);