Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C25 |
| direct product | C22×SD32×C109 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C109 | D8 |
| commutator, Frattini, cosocle | C8 | C24×C109 |
| prime radical | C22×D8×C109 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C109 ◁ C22×C4×C109 ◁ C22×C8×C109 ◁ G | |
400 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 6976 |
A minimal faithful permutation representation — 4 generators on 129 points:
(1,2)(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);(3,4);(5,6,9,13)(7,10,16,19)(8,17,15,12)(11,20,18,14);(6,10)(7,14)(8,15)(11,12)(13,19)(16,20)(17,18)4796 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C109×#13013, C109×#13014, C109×#13018, … |
| maximal normal subgroup of | C109×#13013, C109×#13014, C109×#13018, … |
| maximal quotient of | C22×#357×C109, C22×#358×C109, C22×#367×C109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 2141);