Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#7155 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C59 | D8 |
| commutator | C8 | C4×C8×C59 |
| Frattini, cosocle | C2×C4×C8 | C22×C59 |
| socle | C22×C59 | #340 |
| prime radical | C23×C59 | #106 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
222 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 2 generators on 99 points:
(1,2,3,5,4,6,7,8)(9,10)(11,20)(12,25)(13,28)(14,30)(15,19)(16,21)(17,27)(18,26)(22,32)(23,40)(24,36)(29,33)(31,39)(34,38)(35,37)(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);(9,11,13,22,26,37,27,38,15,24,12,21,14,23,29,39)(10,16,17,20,30,34,28,40,19,32,33,36,18,31,25,35)5192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 143);