Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#33837 |
| 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 ◁ C4×D4×C59 ◁ C8×D4×C59 ◁ G | |
680 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)(6,12)(7,11)(8,16)(9,21)(13,29)(14,31)(15,28)(17,24)(18,33)(19,32)(20,26)(22,25)(27,34)(30,35)(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);(5,6,10,15)(7,13,11,25)(8,18,20,31)(9,22,24,29)(12,17,28,21)(14,32,33,19)(16,35,26,27)(23,30,36,34);(2,4)(5,7,10,11)(6,13,15,25)(8,16,20,26)(9,17,24,21)(12,22,28,29)(14,30,33,34)(18,35,31,27)(19,23,32,36);(5,8,10,20)(6,14,15,33)(7,16,11,26)(9,23,24,36)(12,27,28,35)(13,30,25,34)(17,32,21,19)(18,29,31,22)2537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26825);