Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic269 |
| Sylow | C269 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D269 |
| commutator | C2×C269 | C22×C4 |
| Fitting | C2×Q8×C269 | C2 |
| socle | C22×C269 | C23 |
| hypercenter | C2×Q8 | D269 |
| hypocenter | C269 | C4×Q8 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
70 conjugacy classes of subgroups.
1360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31770690, SD16×Dic269, #31770697, … |
| maximal normal subgroup of | #31770690, SD16×Dic269, #31770697, … |
| maximal quotient of | C4⋊C4×Dic269, #31770491, #31770504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 113);