Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C257 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D257 |
| commutator | C2×C257 | C42 |
| Fitting | C22×C4×C257 | C2 |
| socle | C23×C257 | C22 |
| hypercenter | C22×C4 | D257 |
| hypocenter | C257 | #95 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|a^2=d,b^2=e,b^a=bc,f^b=f^2562068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656471, #30656472, #30656474, … |
| maximal normal subgroup of | #30656471, #30656472, #30656474, … |
| maximal quotient of | #30656491, #30656492, #30656493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 53);