Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2230 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C103 · Schur multiplier (H2) = C2 |
| direct product | C103×#2231 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C103 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C23×C103 |
| prime radical | #135×C103 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C103 ◁ C2×C4×C103 ◁ C4×C8×C103 ◁ G | |
120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 135 |
| transitive degree | μt(G) = 3296 |
A minimal faithful permutation representation — 3 generators on 135 points:
(1,2)(3,14)(4,19,22,30)(5,12)(6,10)(7,13)(8,16)(9,21,27,32)(11,17)(15,29,31,26)(18,25)(20,28,23,24)(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);(1,3,6,17,7,18,5,16)(2,8,12,25,13,11,10,14)(4,15,23,32,22,31,20,21)(9,24,29,19,27,28,26,30);(1,4)(2,9)(3,15)(5,20)(6,23)(7,22)(8,24)(10,26)(11,28)(12,29)(13,27)(14,30)(16,21)(17,32)(18,31)(19,25)2369 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#12463, C103×#12464, C103×#12465, … |
| maximal normal subgroup of | C103×#12463, C103×#12464, C103×#12465, … |
| maximal quotient of | C103×#12824, C103×#12950, C103×#13116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 963);