Finite Group DatabasebetaFinite Group Databasebeta| order | 1328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D83 |
| commutator, socle | C2×C83 | C2×C4 |
| Fitting | C8×C83 | C2 |
| prime radical | C2×D83 | C4 |
| cosocle | C4×C83 | C22 |
| hypercenter | C8 | D83 |
| hypocenter | C83 | M16 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 664 |
Polycyclic presentation:
2^4,83|a^2=c,c^2=d,b^a=bd,e^b=e^82338 conjugacy classes — view the full character table.
| maximal subgroup of | M16×D83, C2×#13050573, #14581798, … |
| maximal normal subgroup of | M16×D83, C2×#13050573, #14581798, … |
| maximal quotient of | #14581702, (C2×D83)⋊C8, Dic83⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1328, 23);