Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C131 · Schur multiplier (H2) = C28 |
| direct product | C2×Q82×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C131 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C131 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16768 |
6550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#8396, C131×#8451, C131×#12777, … |
| maximal normal subgroup of | C131×#8396, C131×#8451, C131×#12777, … |
| maximal quotient of | C2×Q8×C4⋊C4×C131, C2×#2369×C131, C4×Q82×C131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 2209);