Finite Group DatabasebetaFinite Group Databasebeta| order | 17728 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C277 · Schur multiplier (H2) = C25 |
| direct product | C2×C4⋊Q8×C277 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C277 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C277 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C277 ◁ G | |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17728 |
7756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17728, 212);