Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C113 · Schur multiplier (H2) = C25 |
| direct product | C113×#3291 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C113 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C113 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C113 ◁ C2×C4×C113 ◁ G | |
460 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 1808 |
A minimal faithful permutation representation — 4 generators on 129 points:
(1,2,7,12)(3,13,14,15)(4,9,8,16)(5,11,6,10)(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);(1,3)(2,8)(4,12)(5,16)(6,9)(7,14)(10,15)(11,13);(1,4)(2,3)(5,15)(6,13)(7,8)(9,10)(11,16)(12,14);(1,4)(2,9)(3,10)(5,13)(6,15)(7,8)(11,14)(12,16)3277 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C113×#12314, C113×#12315, C113×#12364, … |
| maximal normal subgroup of | C113×#12314, C113×#12315, C113×#12364, … |
| maximal quotient of | C113×#19884, C113×#19888, C113×#19890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 2023);