Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C2×C59×#1532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C2×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C42 | C24×C59 |
| prime radical | C2×#121×C59 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C22×C42×C59 ◁ G | |
1082 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(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);(4,8,9,10)(11,12,15,18,16,19,14,23)(13,20,21,25,22,17,24,26);(3,4)(5,8)(6,10)(7,9)(11,13)(12,17)(14,21)(15,24)(16,22)(18,25)(19,20)(23,26);(3,5,7,6)(4,8,9,10)(11,14,16,15)(12,18,19,23)(13,21,22,24)(17,25,20,26)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 10633);