Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#11759967 |
| Fitting | Q8×C257 ⋊ C4 |
| Sylow | C257 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11759967 |
| commutator, socle | C2×C257 | C22×C4 |
| Fitting | Q8×C257 | C4 |
| hypercenter | Q8 | #11759967 |
| hypocenter | C257 | C4×Q8 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
70 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#11759967, Q16×#11759967, #30657776, … |
| maximal normal subgroup of | SD16×#11759967, Q16×#11759967, #30657776, … |
| maximal quotient of | C4⋊C4×#11759967, #30657686, #30657688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 227);