Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C19×#97 ⋊ C2 |
| Sylow | C19 ⋊ #496 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D76 |
| commutator, cosocle | C2×C4×C19 | C23 |
| Frattini | C2×C4 | C22×D19 |
| Fitting | C19×#97 | C2 |
| socle | C22×C19 | C2×D4 |
| hypercenter | #97 | D19 |
| hypocenter | C19 | #496 |
| LCS | G ▷ C2×C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^18,c^b=cf196 conjugacy classes — view the full character table.
| maximal subgroup of | #14562925, #14562929, #14562930, … |
| maximal normal subgroup of | #14562925, #14562929, #14562930, … |
| maximal quotient of | #14563257, #14563263, #14563274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 938);