Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C53 · Schur multiplier (H2) = C214 |
| direct product | C23×AGL(1,ℤ/8)×C53 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C53 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C26×C53 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ C24×C4×C53 ◁ G | |
13310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 6 generators on 67 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67);(3,4);(5,6);(7,8)(9,11)(10,12)(13,14);(8,11)(9,14)(12,13);(8,12)(11,13)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 56069);