Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C109 · Schur multiplier (H2) = C26 |
| direct product | C109×#3026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C109 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C24×C109 ◁ G | |
800 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 1744 |
A minimal faithful permutation representation — 4 generators on 125 points:
(1,2)(3,6)(4,7)(5,8)(9,15)(10,13)(11,14)(12,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125);(1,3)(2,6)(4,9)(5,10)(7,12)(8,13)(11,16)(14,15);(1,4)(2,7)(3,9)(5,11)(6,12)(8,14)(10,16)(13,15);(2,8)(6,13)(7,14)(12,15)3161 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C109×#23895, C109×#23896, C109×#23996, … |
| maximal normal subgroup of | C109×#23895, C109×#23896, C109×#23996, … |
| maximal quotient of | C109×#18284, C109×#18285, C109×#18286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 1758);