Finite Group DatabasebetaFinite Group Databasebeta| order | 2672 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C167⋊C16 |
| derived, Sylow | C167 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D167 |
| commutator, hypocenter | C167 | C16 |
| Fitting, cosocle | C8×C167 | C2 |
| socle, prime radical | C2×C167 | C8 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 183 |
| transitive degree | μt(G) = 2672 |
Polycyclic presentation:
2^4,167|a^2=b,b^2=c,c^2=d,e^a=e^166680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2672, 15);