Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C113 · Schur multiplier (H2) = C24 |
| direct product | C113×#2980 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C113 | C24 |
| commutator | C22 | C23×C4×C113 |
| Frattini, cosocle | C2×C4 | C24×C113 |
| socle | C22×C113 | C23×C4 |
| prime radical | #532×C113 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ G | |
394 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 7232 |
A minimal faithful permutation representation — 4 generators on 137 points:
(1,2)(3,7)(4,6)(5,8)(9,10,12,16,13,17,20,24)(11,14,19,21,18,15,22,23)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,3)(2,5)(4,8)(6,7)(9,11)(10,14)(12,19)(13,18)(15,17)(16,21)(20,22)(23,24);(3,8)(5,7)(9,11)(10,15)(12,19)(13,18)(14,17)(16,23)(20,22)(21,24);(2,6)(5,7)(11,18)(14,15)(19,22)(21,23)4294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C113×#8918, C113×#9005, C113×#9007, … |
| maximal normal subgroup of | C113×#8918, C113×#9005, C113×#9007, … |
| maximal quotient of | C113×#20532, C113×#20539, C113×#20563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 1712);