Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C257 ⋊ C2 |
| Sylow | C257 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D257 |
| commutator | C4×C257 | C23 |
| Frattini | C4 | C22×D257 |
| Fitting | #41×C257 | C2 |
| socle | C2×C257 | C2×D4 |
| hypercenter | #41 | D257 |
| hypocenter | C257 | #135 |
| LCS | G ▷ C4×C257 ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|c^2=e,d^2=e,b^a=bd,d^a=de,d^b=de,f^b=f^2561294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656851, #30656852, #30656856, … |
| maximal normal subgroup of | #30656851, #30656852, #30656856, … |
| maximal quotient of | #30656731, #30656733, #30656773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 166);