Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D4×C269 ⋊ C2 |
| Sylow | C269 ⋊ #525 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D269 |
| commutator, socle, cosocle | C22×C269 | C24 |
| Frattini | C22 | C23×D269 |
| Fitting | C4×D4×C269 | C2 |
| hypercenter | C4×D4 | D269 |
| hypocenter | C269 | #525 |
| LCS | G ▷ C22×C269 ▷ C269 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^6,269|d^2=e,b^a=be,c^a=cf,g^b=g^2682708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46819574, #46819576, #46819583, … |
| maximal normal subgroup of | #46819574, #46819576, #46819583, … |
| maximal quotient of | #46813266, #46813324, #46813326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1058);