Finite Group DatabasebetaFinite Group Databasebeta| order | 13696 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3026 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C107 · Schur multiplier (H2) = C25×C4 |
| direct product | C107×#3027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C107 | C2×#120 |
| commutator, Frattini, cosocle | C23 | C24×C107 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C107 ◁ C22×C4×C107 ◁ G | |
772 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 212 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) = 1712 |
A minimal faithful permutation representation — 4 generators on 123 points:
(4,11)(6,12)(7,14)(9,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,2)(3,6)(4,7)(5,8)(9,13)(10,12)(11,14)(15,16);(1,3)(2,6)(4,9)(5,10)(7,13)(8,12)(11,15)(14,16);(1,4,5,11)(2,7,8,14)(3,9,10,15)(6,13,12,16)3103 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C107×#13350, C107×#13351, C107×#13353, … |
| maximal normal subgroup of | C107×#13350, C107×#13351, C107×#13353, … |
| maximal quotient of | C107×#18300, C107×#18301, C107×#18302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13696, 1759);