Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C41 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D41 |
| commutator, socle | C2×C41 | C2×C4 |
| Fitting | C2×C4×C41 | C2 |
| prime radical | C22×C41 | C4 |
| cosocle | C4×C41 | C22 |
| hypercenter | C2×C4 | D41 |
| hypocenter | C41 | M16 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^4,41|a^2=c,c^2=d,b^a=bd,e^a=e^40170 conjugacy classes — view the full character table.
| maximal subgroup of | #13050080, #13050081, #13050082, … |
| maximal normal subgroup of | #13050080, #13050081, #13050082, … |
| maximal quotient of | #13050075, C22⋊#66491, C4⋊#66491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 10);