Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C4×C239 ⋊ C2 |
| Sylow | C239 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D239 |
| commutator, socle | C22×C239 | C23 |
| Fitting | C22⋊C4×C239 | C2 |
| hypercenter | C22⋊C4 | D239 |
| hypocenter | C239 | #120 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,239|b^a=bd,c^a=ce,f^a=f^238,f^c=f^2381204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29504960, #120×D239, C2×#21439930, … |
| maximal normal subgroup of | #29504960, #120×D239, C2×#21439930, … |
| maximal quotient of | #29504627, #29504646, #29504647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 116);