Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C113 · Schur multiplier (H2) = C27 |
| direct product | C2×C113×#1905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | #386 |
| commutator | C2×C4 | C23×C4×C113 |
| Frattini, cosocle | C22×C4 | C24×C113 |
| prime radical | C22×#41×C113 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G | |
1678 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 7232 |
A minimal faithful permutation representation — 4 generators on 147 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147);(3,4,8,12,9,14,7,13)(5,15,18,25,19,28,17,10)(6,20,22,11,23,26,21,27)(16,24,31,33,32,34,30,29);(3,5)(4,10,14,25)(6,16)(7,17)(8,18)(9,19)(11,24,27,34)(12,15,13,28)(20,29,26,33)(21,30)(22,31)(23,32);(3,6,9,23)(4,11,14,27)(5,16,19,32)(7,22,8,21)(10,24,25,34)(12,20,13,26)(15,29,28,33)(17,31,18,30)6554 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 13985);