Finite Group DatabasebetaFinite Group Databasebeta| order | 19064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D2383 |
| Fitting | C22×C2383 ⋊ C2 |
| Sylow | C2383 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D2383 |
| commutator, socle, cosocle | C2×C2383 | C22 |
| Fitting | C22×C2383 | C2 |
| hypercenter | C22 | D2383 |
| hypocenter | C2383 | D4 |
| LCS | G ▷ C2×C2383 ▷ C2383 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9532 |
Polycyclic presentation:
2^3,2383|b^a=bc,d^b=d^23824769 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×D2383, C2×C22⋊D2383, #49185733, … |
| maximal normal subgroup of | D4×D2383, C2×C22⋊D2383, #49185733, … |
| maximal quotient of | (C2×D2383)⋊C4, C22⋊Dic2383, Dic2383⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19064, 9);