Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | 2−1+4×C269 ⋊ C2 |
| Sylow | C269 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D269 |
| commutator, socle, cosocle | C2×C269 | C25 |
| Fitting | 2−1+4×C269 | C2 |
| hypercenter | 2−1+4 | D269 |
| hypocenter | C269 | #585 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|e^2=f,b^a=bf,d^a=df,c^b=cf,g^c=g^268,g^d=g^268,g^e=g^2682312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46820232, #46820237, #46820255, … |
| maximal normal subgroup of | #46820232, #46820237, #46820255, … |
| maximal quotient of | #46824085, #46824087, #46824091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1386);