Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D269⋊C32 |
| derived, Sylow | C269 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #11761640 |
| commutator, hypocenter | C269 | C2×C32 |
| Frattini | C8 | C2×#11761640 |
| Fitting | C16×C269 | C4 |
| socle | C2×C269 | C2×C16 |
| prime radical | C2×D269 | C16 |
| cosocle | #16864377 | C22 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^6,269|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^187,g^b=g^268,g^c=g^2681136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#11761640, #46825991, #46826034, … |
| maximal normal subgroup of | C32×#11761640, #46825991, #46826034, … |
| maximal quotient of | #46825990, #46825999, #46826043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1480);