Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C113 · Schur multiplier (H2) = C22 |
| direct product | C113×#7273 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C113 | #333 |
| commutator | C42 | C42×C113 |
| Frattini, cosocle | C2×C4×C8 | C22×C113 |
| socle | C2×C113 | #1296 |
| prime radical | C23×C113 | #101 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C113 ◁ C22×C4×C113 ◁ C2×C4×C8×C113 ◁ G | |
208 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 145 |
| transitive degree | μt(G) = 3616 |
A minimal faithful permutation representation — 2 generators on 145 points:
(1,2,4,9,6,8,18,11)(3,12,14,7,16,21,13,23)(5,19,17,10,20,25,28,24)(15,22,29,31,30,32,27,26)(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);(1,3,5,15,4,13,17,27,6,16,20,30,18,14,28,29)(2,7,10,22,11,21,19,31,8,23,24,32,9,12,25,26)5198 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 261);