Finite Group DatabasebetaFinite Group Databasebeta| order | 1328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C83 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D83 |
| commutator, socle | C2×C83 | C2×C4 |
| Fitting | C2×C4×C83 | C2 |
| prime radical | C22×C83 | C4 |
| cosocle | C4×C83 | C22 |
| hypercenter | C2×C4 | D83 |
| hypocenter | C83 | M16 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 664 |
Polycyclic presentation:
2^4,83|a^2=c,c^2=d,b^a=bd,e^a=e^82338 conjugacy classes — view the full character table.
| maximal subgroup of | #14581708, #14581709, #14581710, … |
| maximal normal subgroup of | #14581708, #14581709, #14581710, … |
| maximal quotient of | #14581703, C22⋊(C83⋊C8), C4⋊(C83⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1328, 24);