Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C101 · Schur multiplier (H2) = C24 |
| direct product | C101×#9086 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C101 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C101 |
| Frattini, cosocle | C23×C4 | C23×C101 |
| prime radical | C24×C101 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ C22×C42×C101 ◁ G | |
604 conjugacy classes of subgroups.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 3 generators on 129 points:
(1,2)(3,4)(5,6,9,11,8,7,10,12)(13,14)(15,18,22,25)(16,19)(17,20)(21,24,27,28)(23,26)(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);(5,7,9,12,8,6,10,11)(13,15,17,22)(14,18)(16,21,23,27)(19,24)(20,25)(26,28);(2,4)(6,7)(11,12)(13,16,17,23)(14,19,20,26)(15,21,22,27)(18,24,25,28)5252 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 2074);