Finite Group DatabasebetaFinite Group Databasebeta| order | 25856 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C101 · Schur multiplier (H2) = C24 |
| direct product | C101×#17838 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C101 | C22×D4 |
| commutator | C2×C4 | C23×C4×C101 |
| Frattini, cosocle | C42 | C24×C101 |
| socle | C22×C101 | C22×C4⋊C4 |
| prime radical | C2×#41×C101 | Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C101 ◁ C4×#41×C101 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 4 generators on 133 points:
(2,6)(4,12)(7,13)(8,14)(9,16)(11,15)(17,18,21,24,22,25,20,30)(19,26,29,31,27,32,28,23)(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);(1,2,4,6,5,8,12,14)(3,9,11,16,10,7,15,13)(17,19,20,28,22,27,21,29)(18,23,24,26,25,31,30,32);(1,3)(2,7)(4,11)(5,10)(6,13)(8,9)(12,15)(14,16)(19,27)(23,31)(26,32)(28,29);(3,10)(7,9)(11,15)(13,16)5858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25856, 10826);