Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C103 · Schur multiplier (H2) = C23 |
| direct product | C103×#2056 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C103 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C103 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G | |
288 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 13184 |
A minimal faithful permutation representation — 3 generators on 127 points:
(1,2)(3,4)(9,10,14,18)(11,19,12,22)(13,24,20,17)(15,23,16,21)(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);(5,6)(7,8)(9,11,14,12)(10,15,18,16)(13,23,20,21)(17,22,24,19);(2,4)(6,8)(9,12,13,23,14,11,20,21)(10,16,17,22,18,15,24,19)3296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#7082, C103×#7090, C103×#12161, … |
| maximal normal subgroup of | C103×#7082, C103×#7090, C103×#12161, … |
| maximal quotient of | C103×#10478, C103×#10479, C103×#10482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 788);