Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C101 ⋊ C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D101 |
| commutator | C2×C101 | C2×C42 |
| Fitting | #95×C101 | C2 |
| socle | C23×C101 | C23 |
| hypercenter | #95 | D101 |
| hypocenter | C101 | C4×C4⋊C4 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ #95 | |
194 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=e,b^2=f,c^2=de,b^a=bd,g^c=g^1001040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27169625, #27169629, #27169654, … |
| maximal normal subgroup of | #27169625, #27169629, #27169654, … |
| maximal quotient of | #95×Dic101, #27169356, #27169360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 400);