Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C26 |
| direct product | C61×#33554 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C61 |
| prime radical | C61×#3025 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×#41×C61 ◁ G | |
1112 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 4 generators on 93 points:
(1,2)(3,11)(4,8)(5,9)(6,10)(7,13)(12,25)(14,26)(15,29)(16,22)(17,23)(18,24)(19,27)(20,28)(21,30)(31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(1,3,6,14)(2,7,10,20)(4,15,17,12)(5,13,18,28)(8,21,23,19)(9,11,24,26)(16,30,31,27)(22,29,32,25);(5,18)(13,28)(16,31)(27,30);(1,4,6,17)(2,8,10,23)(3,12,14,15)(5,16,18,31)(7,19,20,21)(9,22,24,32)(11,25,26,29)(13,27,28,30)2074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26542);