Finite Group DatabasebetaFinite Group Databasebeta| order | 6064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C379 ⋊ C2 |
| Sylow | C379 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D379 |
| commutator | C4×C379 | C22 |
| Frattini | C4 | C2×D379 |
| Fitting | Q8×C379 | C2 |
| socle | C2×C379 | D4 |
| hypercenter | Q8 | D379 |
| hypocenter | C379 | SD16 |
| LCS | G ▷ C4×C379 ▷ C2×C379 ▷ C379 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,379|a^2=d,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 | SD16×D379, C2×#20258593, #27131351, … |
| maximal normal subgroup of | SD16×D379, C2×#20258593, #27131351, … |
| maximal quotient of | #27131251, #27131255, #27131262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6064, 27);