Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C109 · Schur multiplier (H2) = C22 |
| direct product | C109×#1319 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | #99 |
| commutator | C2×C4 | C2×C8×C109 |
| Frattini, cosocle | C2×C4⋊C4 | C22×C109 |
| prime radical | C23×C109 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C23×C109 ◁ C2×C4⋊C4×C109 ◁ G | |
134 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 3488 |
A minimal faithful permutation representation — 2 generators on 133 points:
(1,2,3,5,4,6,7,8)(9,10)(11,17,19,24)(12,20,22,15)(13,16)(14,18)(21,23)(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);(9,11,13,19)(10,14,16,23)(12,21,22,18)(15,24,20,17)2834 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C109×#7345, C109×#7376, C109×#7404, … |
| maximal normal subgroup of | C109×#7345, C109×#7376, C109×#7404, … |
| maximal quotient of | C109×#7057, C109×#7061, C109×#7104, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 51);