Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16×C53 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×C16×C53 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C16×C53 | C22 |
| commutator | C2 | C23×C16×C53 |
| Frattini, cosocle | C2×C8 | C24×C53 |
| socle, prime radical | C23×C53 | C22×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C16×C53 ◁ G | |
582 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 4 generators on 79 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(11,12,13,16,14,17,19,22,15,18,20,23,21,24,25,26);(3,4,6,8)(5,9,10,7);(3,5,6,10)(4,7,8,9)8480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 26460);