Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C113 · Schur multiplier (H2) = C22 |
| direct product | C113×#1657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C113 |
| prime radical | #496×C113 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C42×C113 ◁ G | |
206 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 206 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) = 137 |
| transitive degree | μt(G) = 7232 |
A minimal faithful permutation representation — 3 generators on 137 points:
(2,5)(3,7)(6,8)(10,15)(11,18)(12,13)(17,20)(19,21)(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);(3,7)(5,8)(9,10)(11,16)(12,20)(13,15)(14,17)(18,23)(19,24)(21,22);(1,2)(3,8)(4,6)(5,7)(9,11,14,19)(10,16,17,24)(12,18,13,21)(15,22,20,23)2260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C113×#13679, C2×C113×#1657, C113×#18984, … |
| maximal normal subgroup of | C113×#13679, C2×C113×#1657, C113×#18984, … |
| maximal quotient of | C113×#7736, C113×#7738, C113×#7740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 389);