Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C257 ⋊ C2 |
| Sylow | C257 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D257 |
| commutator, socle | C2×C257 | C24 |
| Fitting | #41×C257 | C2 |
| hypercenter | #41 | D257 |
| hypocenter | C257 | H(5,𝔽2) |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|b^a=be,d^a=de,c^b=ce,f^c=f^256,f^d=f^2561297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656903, #30656906, #30656913, … |
| maximal normal subgroup of | #30656903, #30656906, #30656913, … |
| maximal quotient of | #30657209, #30657211, #30657217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 192);