Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C103 · Schur multiplier (H2) = C2×C4 |
| direct product | C103×#1634 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C103 |
| prime radical | #555×C103 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C42×C103 ◁ G | |
218 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 6592 |
A minimal faithful permutation representation — 3 generators on 127 points:
(2,5)(3,7)(6,8)(9,10,13,17)(11,18,21,24)(12,15,22,16)(14,19,23,20)(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);(3,7)(5,8)(9,11,13,21)(10,14,17,23)(12,19,22,20)(15,18,16,24);(1,2,4,6)(3,8,7,5)(9,12,13,22)(10,15,17,16)(11,19,21,20)(14,18,23,24)2678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#7521, C103×#13682, C2×C103×#1634, … |
| maximal normal subgroup of | C103×#7521, C103×#13682, C2×C103×#1634, … |
| maximal quotient of | C103×#7758, C103×#7760, C103×#7785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 366);