Finite Group DatabasebetaFinite Group Databasebeta| order | 13184 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C103 · Schur multiplier (H2) = C26 |
| direct product | C2×#458×C103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C103 | #120 |
| commutator, Frattini, cosocle | C23 | C24×C103 |
| prime radical | C2×H(5,𝔽2)×C103 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C103 ◁ C24×C103 ◁ G | |
794 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 794 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) = 121 |
| transitive degree | μt(G) = 3296 |
A minimal faithful permutation representation — 4 generators on 121 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103)(104,105);(106,107,110,113)(108,111,115,118)(109,112,116,119)(114,120,121,117);(106,108)(107,111)(109,114)(110,115)(112,117)(113,118)(116,121)(119,120);(106,109)(107,112)(108,114)(110,116)(111,117)(113,119)(115,121)(118,120)3296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C103×#13042, C103×#13044, C103×#13344, … |
| maximal normal subgroup of | C103×#13042, C103×#13044, C103×#13344, … |
| maximal quotient of | C2×C103×#1607, C2×C103×#1613, C2×C103×#1608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 1756);