Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#33610 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×#41×C59 ◁ C2×#131×C59 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 95 points:
(1,2)(3,4)(5,6)(7,16)(8,13)(9,24)(10,22)(11,15)(12,19)(14,17)(18,29)(20,35)(21,31)(23,28)(25,36)(26,33)(27,34)(30,32)(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);(5,7,17,32,10,20,25,34,11,21,23,33,8,18,9,19)(6,12,24,29,13,26,28,31,15,27,36,35,22,30,14,16);(2,4)(5,6)(7,12)(8,22)(9,14)(10,13)(11,15)(16,19)(17,24)(18,30)(20,26)(21,27)(23,36)(25,28)(29,32)(31,34)(33,35);(5,8,11,10)(6,13,15,22)(7,18,21,20)(9,23,25,17)(12,26,27,30)(14,24,28,36)(16,29,31,35)(19,33,34,32)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26598);