Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#16861593 |
| derived, Sylow | C257 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D257 |
| commutator, hypocenter | C257 | C22×C16 |
| Frattini | C8 | C22×D257 |
| Fitting | C22×C8×C257 | C2 |
| socle, prime radical | C23×C257 | C8 |
| cosocle | C8×C257 | C23 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16448 |
4160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45662397, #45662398, #45662409, … |
| maximal normal subgroup of | #45662397, #45662398, #45662409, … |
| maximal quotient of | C2×C4×#16861593, C2×C22⋊#16861593, C2×C4⋊#16861593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 961);