Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D92 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C92 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D92 |
| commutator, hypocenter | C92 | C2×C8 |
| Frattini | C32×C4 | D32 |
| Fitting, cosocle | C4×C92 | C22 |
| socle | C2×C32 | #624 |
| prime radical | C2×C9⋊D9 | C4 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C4 | |
155 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^4|a^2=c,b^2=c,c^2=d,e^3=h,f^3=g,f^a=f^2g^2,g^a=g^2,e^b=e^2h^2,h^b=h^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #72219866, #72219891, #72219899, … |
| maximal normal subgroup of | #72219866, #72219891, #72219899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 79);