Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C239 ⋊ #108 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D239 |
| commutator | C4×C239 | C2×C4 |
| Frattini | C2×C4 | C2×D239 |
| Fitting | M16×C239 | C2 |
| socle | C2×C239 | C4⋊C4 |
| hypercenter | M16 | D239 |
| hypocenter | C239 | #108 |
| LCS | G ▷ C4×C239 ▷ C2×C239 ▷ C239 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ M16 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,239|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^b=f^2381204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #108×D239, C2×#21439895, #29504819, … |
| maximal normal subgroup of | #108×D239, C2×#21439895, #29504819, … |
| maximal quotient of | #29504522, #29504524, #29504536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 81);