Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C269⋊#401 |
| Sylow | C269 ⋊ #401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D269 |
| commutator, socle, prime radical, cosocle | C23×C269 | C23 |
| Fitting | #95×C269 | C2 |
| hypercenter | #95 | D269 |
| hypocenter | C269 | #401 |
| LCS | G ▷ C23×C269 ▷ C269 | |
| UCS | C1 ◁ C23 ◁ #95 | |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^6,269|a^2=def,b^2=de,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^2682702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #401×D269, C2×C269⋊#401, #46814182, … |
| maximal normal subgroup of | #401×D269, C2×C269⋊#401, #46814182, … |
| maximal quotient of | #46809145, #46809146, #46809147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 492);