Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic239 |
| Sylow | C239 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D239 |
| commutator | C2×C239 | C22×C4 |
| Fitting | C2×D4×C239 | C2 |
| socle | C22×C239 | C23 |
| hypercenter | C2×D4 | D239 |
| hypocenter | C239 | C4×D4 |
| LCS | G ▷ C2×C239 ▷ C239 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29504852, D8×Dic239, SD16×Dic239, … |
| maximal normal subgroup of | #29504852, D8×Dic239, SD16×Dic239, … |
| maximal quotient of | C22⋊C4×Dic239, C4⋊C4×Dic239, #29504647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 109);