Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2215 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C61 · Schur multiplier (H2) = C24 |
| direct product | C2×C61×#2253 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C61 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C61 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ C2×C4×C8×C61 ◁ G | |
494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 15616 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(3,4,6,8)(5,9,10,7)(11,12,14,17)(13,21,23,35)(15,28,26,41)(16,29,27,20)(18,32,30,24)(19,34,31,22)(25,40,39,37)(33,38,36,42);(3,5,6,10)(4,7,8,9)(12,17)(18,30)(19,31)(20,29)(21,35)(28,41)(33,36)(37,40);(11,13,22,38,16,25,26,32,14,23,34,42,27,39,15,24)(12,18,28,37,20,33,31,35,17,30,41,40,29,36,19,21)4636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 26712);