Finite Group DatabasebetaFinite Group Databasebeta| order | 6064 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic379 |
| Sylow | C379 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D379 |
| commutator | C2×C379 | C2×C4 |
| Fitting | C2×C4×C379 | C2 |
| socle | C22×C379 | C22 |
| hypercenter | C2×C4 | D379 |
| hypocenter | C379 | C4⋊C4 |
| LCS | G ▷ C2×C379 ▷ C379 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,379|a^2=d,b^2=c,b^a=bc,e^a=e^3781522 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27131252, #27131253, #27131255, … |
| maximal normal subgroup of | #27131252, #27131253, #27131255, … |
| maximal quotient of | C379⋊#95, C4⋊(C379⋊C8), #27131263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6064, 20);