Finite Group DatabasebetaFinite Group Databasebeta| order | 28928 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C113 · Schur multiplier (H2) = C22×C4 |
| direct product | C8×#101×C113 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C113 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C113 |
| Frattini, cosocle | C2×C42 | C23×C113 |
| socle | C22×C113 | C4×C22⋊C4 |
| prime radical | C23×C113 | C2×C42 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C113 ◁ C2×C4×C8×C113 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 14464 |
A minimal faithful permutation representation — 3 generators on 137 points:
(1,2,3,5,4,6,7,8)(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);(9,10,12,16,13,15,21,23)(11,17,18,24,19,14,20,22);(9,11,13,19)(10,14,15,17)(12,20,21,18)(16,24,23,22)9944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28928, 1151);