Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C109 · Schur multiplier (H2) = C24 |
| direct product | C109×#1912 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | #386 |
| commutator | C2×C4 | C22×C4×C109 |
| Frattini, cosocle | C22×C4 | C23×C109 |
| prime radical | C2×#41×C109 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C22×C4×C109 ◁ G | |
314 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 3 generators on 141 points:
(1,2,6,10,7,11,5,21)(3,12,16,23,15,27,14,8)(4,17,19,25,20,9,18,24)(13,26,30,22,29,32,28,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,3)(2,8,11,23)(4,13)(5,14)(6,16)(7,15)(9,22,17,31)(10,12,21,27)(18,28)(19,30)(20,29)(24,32,25,26);(1,4,7,20)(2,9,11,17)(3,13,15,29)(5,19,6,18)(8,22,23,31)(10,25,21,24)(12,26,27,32)(14,30,16,28)3161 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C109×#12781, C109×#12782, C2×C109×#1912, … |
| maximal normal subgroup of | C109×#12781, C109×#12782, C2×C109×#1912, … |
| maximal quotient of | C109×#9100, C109×#9102, C109×#9104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 644);