Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C41 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D41 |
| commutator | C2×C41 | C2×C4 |
| Fitting | C2×C4×C41 | C2 |
| socle, prime radical, cosocle | C22×C41 | C22 |
| hypercenter | C2×C4 | D41 |
| hypocenter | C41 | C4⋊C4 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^4,41|a^2=d,b^2=c,b^a=bd,e^a=e^40170 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C4×D41, C2×#10620279, #13050120, … |
| maximal normal subgroup of | C4⋊C4×D41, C2×#10620279, #13050120, … |
| maximal quotient of | #13050071, #13050093, #13050095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 12);