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×#2237 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C109 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C109 |
| prime radical | C23×C109 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C109 ◁ C22×C4×C109 ◁ C22×C8×C109 ◁ G | |
132 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 6976 |
A minimal faithful permutation representation — 3 generators on 149 points:
(1,2)(3,6)(4,5)(7,8)(9,10,14,19)(11,15,22,30)(12,16,25,32)(13,26,24,18)(17,33,31,23)(20,27,36,39)(21,37,35,29)(28,40,38,34)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149);(2,5)(6,8)(9,11,14,22)(10,15,19,30)(12,20,25,36)(13,21,24,35)(16,27,32,39)(17,28,31,38)(18,29,26,37)(23,34,33,40);(1,3,4,7)(2,6,5,8)(10,16)(12,23)(13,24)(15,27)(17,18)(19,32)(20,34)(21,35)(25,33)(26,31)(28,29)(30,39)(36,40)(37,38)3161 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C109×#2237, C109×#33645, C109×#33647, … |
| maximal normal subgroup of | C2×C109×#2237, C109×#33645, C109×#33647, … |
| maximal quotient of | C109×#12868, C109×#12921, C109×#12994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 969);