Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C59 · Schur multiplier (H2) = C4 |
| direct product | C59×#7356 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | #353 |
| commutator | C42 | C2×C8×C59 |
| Frattini, cosocle | #423 | C22×C59 |
| socle | C2×C59 | #1318 |
| prime radical | C59×#532 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C59×#423 ◁ G | |
202 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 2 generators on 91 points:
(1,2,4,9,5,8,20,26,6,11,18,28,21,10,19,29)(3,12,13,27,15,7,22,23,16,24,30,32,14,25,17,31)(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);(1,3)(2,7)(4,17)(5,15)(6,16)(8,24)(9,27)(10,12)(11,25)(13,20)(14,21)(18,22)(19,30)(23,26)(28,32)(29,31)1652 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 344);