Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C103 · Schur multiplier (H2) = C24×C4 |
| direct product | C103×#3150 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C103 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C103 |
| socle | C22×C103 | C22×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G | |
564 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 6592 |
A minimal faithful permutation representation — 4 generators on 123 points:
(2,4)(5,6)(7,14)(8,11)(9,13)(10,16)(12,17)(15,19)(18,20)(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);(5,7,8,16,9,15,17,20)(6,10,12,14,13,18,11,19);(1,2,3,4)(7,15)(10,18)(14,19)(16,20);(5,8,9,17)(6,11,13,12)(7,16,15,20)(10,19,18,14)3296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#9007, C103×#10032, C103×#10034, … |
| maximal normal subgroup of | C103×#9007, C103×#10032, C103×#10034, … |
| maximal quotient of | C103×#19608, C103×#19613, C103×#19616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 1882);