Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C113 · Schur multiplier (H2) = C22 |
| direct product | C113×#1352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C113 | #99 |
| commutator | C22×C4 | C2×C4×C113 |
| Frattini, cosocle | C2×C22⋊C4 | C22×C113 |
| prime radical | C24×C113 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C113 ◁ C23×C113 ◁ C2×C22⋊C4×C113 ◁ G | |
154 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 129 |
| transitive degree | μt(G) = 3616 |
A minimal faithful permutation representation — 2 generators on 129 points:
(2,5,6,7)(9,10)(11,14,16,13)(12,15)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129);(1,2)(3,7)(4,6)(5,8)(10,13,15,14)2599 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C113×#1352, C113×#11715, C113×#11716, … |
| maximal normal subgroup of | C2×C113×#1352, C113×#11715, C113×#11716, … |
| maximal quotient of | C113×#7123, C113×#7132, C113×#7250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 84);