Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C113 · Schur multiplier (H2) = C2 |
| direct product | C113×#1676 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C113 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C113 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C42×C113 ◁ G | |
144 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 145 |
| transitive degree | μt(G) = 14464 |
A minimal faithful permutation representation — 3 generators on 145 points:
(1,2,5,8)(3,9,12,16)(4,13,10,7)(6,14,15,11)(17,18,21,24)(19,25,27,32)(20,28,30,23)(22,29,31,26)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(1,3,10,14,5,12,4,11)(2,6,13,16,8,15,7,9);(17,19,21,27)(18,22,24,31)(20,29,30,26)(23,32,28,25)3277 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C113×#12384, C113×#12385, C113×#12386, … |
| maximal normal subgroup of | C113×#12384, C113×#12385, C113×#12386, … |
| maximal quotient of | C113×#8645, C113×#9216, C113×#9568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 408);