Finite Group DatabasebetaFinite Group Databasebeta| order | 19216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic1201 |
| derived, Sylow | C1201 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D1201 |
| commutator, hypocenter | C1201 | C22×C4 |
| Frattini | C2 | C22×D1201 |
| Fitting, socle, prime radical | C23×C1201 | C2 |
| cosocle | C2×C1201 | C23 |
| LCS | G ▷ C1201 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19216 |
4816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50307761, C2×C4×Dic1201, C2×#34063500, … |
| maximal normal subgroup of | #50307761, C2×C4×Dic1201, C2×#34063500, … |
| maximal quotient of | C2×C4×Dic1201, C2×C22⋊Dic1201, C2×C4⋊Dic1201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19216, 33);