Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C113 · Schur multiplier (H2) = C22 |
| direct product | C113×#7116 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | #329 |
| commutator | C42 | C2×C8×C113 |
| Frattini, cosocle | C2×#97 | C22×C113 |
| prime radical | C2×#127×C113 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C22×C4×C113 ◁ C2×#97×C113 ◁ G | |
282 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 3616 |
A minimal faithful permutation representation — 2 generators on 137 points:
(1,2)(3,7,8,5)(4,6)(9,10,11,17,13,16,19,23,14,18,20,24,12,15,21,22)(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);(1,3)(2,5)(4,8)(6,7)(10,15)(11,19)(12,13)(16,18)(17,24)(20,21)4520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 104);