Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C113 · Schur multiplier (H2) = C23 |
| direct product | C2×#358×C113 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C113 | D8 |
| commutator | C8 | C22×C4×C113 |
| Frattini, cosocle | C2×C8 | C23×C113 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C113 ◁ C22×C4×C113 ◁ C22×C8×C113 ◁ G | |
232 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 14464 |
A minimal faithful permutation representation — 3 generators on 135 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135);(3,4,5,6)(8,12)(9,15)(10,17)(13,22)(14,21)(16,19)(18,20);(7,8,11,14)(9,16,18,22)(10,19,17,13)(12,20,21,15)4972 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#358×C113, C113×#12638, C113×#12732, … |
| maximal normal subgroup of | C4×#358×C113, C113×#12638, C113×#12732, … |
| maximal quotient of | C2×C113×#1332, C113×#11646, C113×#11658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 869);