Finite Group DatabasebetaFinite Group Databasebeta| order | 17216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#16864405 |
| derived, Sylow | C269 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #11761640 |
| commutator, hypocenter | C269 | C22×C16 |
| Frattini | C4 | C22×#11761640 |
| Fitting | C22×C4×C269 | C4 |
| socle, prime radical | C23×C269 | C8 |
| cosocle | #14524130 | C23 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17216 |
1136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46825923, #46825924, #46825939, … |
| maximal normal subgroup of | #46825923, #46825924, #46825939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17216, 1602);