Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#33552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C59 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C23×C59 ◁ C22×D4×C59 ◁ G | |
1156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,11)(4,8)(5,9)(6,10)(7,14)(12,24)(13,25)(15,21)(16,22)(17,30)(18,23)(19,27)(20,28)(26,32)(29,31)(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)(4,12)(5,14)(6,13)(8,19)(9,11)(10,20)(15,27)(16,26)(17,29)(18,28)(21,24)(22,31)(23,25)(30,32);(1,4,6,16)(2,8,10,22)(3,12,13,26)(5,17,18,15)(7,19,20,31)(9,21,23,30)(11,24,25,32)(14,29,28,27);(3,13)(7,20)(11,25)(12,26)(14,28)(19,31)(24,32)(27,29)2006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26540);