Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C101 ⋊ C2 |
| Sylow | C101 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D101 |
| commutator | C2×C101 | C22×C8 |
| Frattini | C2×C4 | C22×D101 |
| Fitting | C4×C8×C101 | C2 |
| socle | C22×C101 | C22×C4 |
| hypercenter | C4×C8 | D101 |
| hypocenter | C101 | #431 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^1001640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13108057, #27169411, #27169414, … |
| maximal normal subgroup of | C8×#13108057, #27169411, #27169414, … |
| maximal quotient of | #27170877, C4×#15692167, C4×#15692184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 600);