Finite Group DatabasebetaFinite Group Databasebeta| order | 6064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C379 ⋊ C2 |
| Sylow | C379 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D379 |
| commutator | C4×C379 | C22 |
| Frattini | C4 | C2×D379 |
| Fitting | D4×C379 | C2 |
| socle | C2×C379 | D4 |
| hypercenter | D4 | D379 |
| hypocenter | C379 | D8 |
| LCS | G ▷ C4×C379 ▷ C2×C379 ▷ C379 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,379|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^378952 conjugacy classes — view the full character table.
| maximal subgroup of | D8×D379, C2×#20258591, #27131351, … |
| maximal normal subgroup of | D8×D379, C2×#20258591, #27131351, … |
| maximal quotient of | #27131251, #27131252, #27131264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6064, 25);