Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C113 · Schur multiplier (H2) = C24 |
| direct product | C113×#22249 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C113 | C22×D4 |
| commutator | C2×C4 | C23×C4×C113 |
| Frattini, cosocle | C22×C4 | C24×C113 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C43×C113 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 28928 |
A minimal faithful permutation representation — 4 generators on 149 points:
(1,2,4,3)(5,6)(7,14)(8,12)(9,18)(10,13)(11,16)(15,20)(17,19)(21,22)(23,29)(24,26)(25,33)(27,32)(28,31)(30,35)(34,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149);(1,3,4,2)(5,7)(6,11)(8,17)(9,15)(10,16)(12,20)(13,14)(18,19)(22,26)(23,30)(28,33)(32,36);(5,8,10,9)(6,12,13,18)(7,15,16,17)(11,19,14,20)(21,23,31,36,24,30,25,32)(22,27,33,35,26,34,28,29);(5,9,10,8)(6,12,13,18)(7,15,16,17)(11,20,14,19)(22,26)(27,34)(28,33)(29,35)7232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 15237);