Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C257 ⋊ C2 |
| Sylow | C257 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D257 |
| commutator, socle | C2×C257 | C22×C4 |
| Fitting | M16×C257 | C2 |
| hypercenter | M16 | D257 |
| hypocenter | C257 | #131 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|a^2=d,d^2=e,f^a=f^256,c^b=ce,f^c=f^2561300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656851, #30656853, #30656856, … |
| maximal normal subgroup of | #30656851, #30656853, #30656856, … |
| maximal quotient of | #30656694, #30656695, #30656702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 154);