Finite Group DatabasebetaFinite Group Databasebeta| order | 6736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C421 ⋊ C2 |
| Sylow | C421 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D421 |
| commutator, socle | C2×C421 | C2×C4 |
| Fitting | C8×C421 | C2 |
| hypercenter | C8 | D421 |
| hypocenter | C421 | M16 |
| LCS | G ▷ C2×C421 ▷ C421 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,421|a^2=c,c^2=d,b^a=bd,e^b=e^4201690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×D421, C2×#20269754, #27212372, … |
| maximal normal subgroup of | M16×D421, C2×#20269754, #27212372, … |
| maximal quotient of | #27212276, #27212278, #27212295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6736, 23);