Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C239 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D239 |
| commutator, socle | C22×C239 | C23 |
| Fitting | C22×C4×C239 | C2 |
| hypercenter | C22×C4 | D239 |
| hypocenter | C239 | C22⋊Q8 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,239|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^2381918 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29504508, #29504510, #29504923, … |
| maximal normal subgroup of | #29504508, #29504510, #29504923, … |
| maximal quotient of | #29504632, #29504645, #29504656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 125);