Finite Group DatabasebetaFinite Group Databasebeta| order | 6752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C42×C211 ⋊ C2 |
| Sylow | C211 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D211 |
| commutator | C2×C211 | C22×C4 |
| Frattini | C22 | C22×D211 |
| Fitting | C42×C211 | C2 |
| socle | C22×C211 | C23 |
| hypercenter | C42 | D211 |
| hypocenter | C211 | #117 |
| LCS | G ▷ C2×C211 ▷ C211 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,211|a^2=e,c^2=d,b^a=bd,f^b=f^2101700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27213100, #27213103, #27213161, … |
| maximal normal subgroup of | #27213100, #27213103, #27213161, … |
| maximal quotient of | #27212992, C4×(C2×D211)⋊C4, C4×Dic211⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6752, 103);