Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#1907 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #121 |
| commutator | C2×C4 | C22×C4×C109 |
| Frattini, cosocle | C22×C4 | C23×C109 |
| prime radical | C2×AGL(1,ℤ/8)×C109 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ G | |
332 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 3 generators on 129 points:
(1,2)(3,4)(5,6,10,12,9,8,14,17)(7,13,15,20,16,11,18,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129);(5,7,14,15,9,16,10,18)(6,11,12,20,8,13,17,19);(2,4)(5,8)(6,9)(7,13)(10,12)(11,16)(14,17)(15,19)(18,20)3488 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C109×#1907, C109×#21003, C109×#21004, … |
| maximal normal subgroup of | C2×C109×#1907, C109×#21003, C109×#21004, … |
| maximal quotient of | C109×#9095, C109×#9097, C109×#9163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 639);