Finite Group DatabasebetaFinite Group Databasebeta| order | 1444 |
| isoclinism | isoclinic class of #13089659 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C192 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C192 | C4 |
| prime radical, cosocle | C19⋊D19 | C2 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 38 |
Polycyclic presentation:
2^2,19^2|a^2=b,c^a=c^12d^10,d^a=c^14d^7,c^b=c^18,d^b=d^1894 conjugacy classes — view the full character table.
| maximal subgroup of | #16864578, #13089659⋊C3, C3×#13089659, … |
| maximal normal subgroup of | #13089659⋊C3, C3×#13089659, C11×#13089659, … |
| maximal quotient of | C3×#13089659, C3⋊#13089659, #27188946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1444, 8);