Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C109 · Schur multiplier (H2) = C2 |
| direct product | C109×#2227 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C109 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C109 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C42×C109 ◁ C4×C8×C109 ◁ G | |
130 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 13952 |
A minimal faithful permutation representation — 3 generators on 133 points:
(1,2,4,6)(3,7,8,5)(10,14)(11,17)(13,20)(15,23)(16,19)(18,24)(21,22)(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);(1,3,4,8)(2,5,6,7)(9,10,12,14)(11,15,18,22)(13,16,19,20)(17,21,24,23);(9,11,12,18)(10,15,14,22)(13,21,19,23)(16,24,20,17)3161 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C109×#12373, C109×#12374, C109×#12379, … |
| maximal normal subgroup of | C109×#12373, C109×#12374, C109×#12379, … |
| maximal quotient of | C109×#12812, C109×#12936, C109×#13112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 959);