Finite Group DatabasebetaFinite Group Databasebeta| order | 13952 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2202 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C109 · Schur multiplier (H2) = C23 |
| direct product | C109×#2203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C109 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C23×C109 |
| prime radical | #454×C109 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C109 ◁ C22×C109 ◁ C2×Q8×C109 ◁ G | |
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
A minimal faithful permutation representation — 3 generators on 141 points:
(1,2)(3,12)(4,16)(5,8)(6,11)(7,13)(9,19)(10,21)(14,29)(15,27)(17,25)(18,26)(20,30)(22,28)(23,31)(24,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,3,6,15)(2,7,11,25)(4,17,19,13)(5,20,21,14)(8,23,10,24)(9,27,16,12)(18,31,22,32)(26,29,28,30);(2,8)(5,21)(7,23)(9,28)(10,11)(12,29)(14,20)(16,26)(18,22)(24,25)(27,30)(31,32)1853 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C109×#13679, C109×#13680, C2×C109×#2203, … |
| maximal normal subgroup of | C109×#13679, C109×#13680, C2×C109×#2203, … |
| maximal quotient of | C109×#12097, C109×#12098, C109×#12126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13952, 935);