Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C103 · Schur multiplier (H2) = C22 |
| direct product | C103×#2214 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C103 | #459 |
| 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 | |
150 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 150 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:
(1,2,6,10)(3,11,15,29)(4,16,20,32)(5,21,12,9)(7,22,24,14)(8,25,28,18)(13,26,30,27)(17,23,19,31)(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);(1,3,12,22,6,15,5,14)(2,7,21,29,10,24,9,11)(4,13,19,25,20,30,17,18)(8,23,27,32,28,31,26,16);(1,4)(2,8)(3,13)(5,17)(6,20)(7,23)(9,26)(10,28)(11,16)(12,19)(14,18)(15,30)(21,27)(22,25)(24,31)(29,32)2369 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#12312, C103×#12313, C103×#12315, … |
| maximal normal subgroup of | C103×#12312, C103×#12313, C103×#12315, … |
| maximal quotient of | C103×#12422, C103×#12423, C103×#12426, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 946);