Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×Q32 ⋊ C2 |
| Sylow | C19 ⋊ #508 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D19 |
| commutator, cosocle | C8×C19 | C23 |
| Frattini | C8 | C22×D19 |
| Fitting | C19×Q32 | C2 |
| socle | C2×C19 | C2×D8 |
| hypercenter | Q32 | D19 |
| hypocenter | C19 | #508 |
| LCS | G ▷ C8×C19 ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^18,d^b=de,e^b=ef,g^b=g^18,g^c=g^18121 conjugacy classes — view the full character table.
| maximal subgroup of | #14565943, #14565945, #14565949, … |
| maximal normal subgroup of | #14565943, #14565945, #14565949, … |
| maximal quotient of | #14565341, #14565416, #14565481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 982);