Finite Group DatabasebetaFinite Group Databasebeta| order | 6064 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D379 |
| Fitting | C8×C379 ⋊ C2 |
| derived, Sylow | C379 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D379 |
| commutator, hypocenter | C379 | C2×C8 |
| Frattini | C4 | C2×D379 |
| Fitting | C8×C379 | C2 |
| socle | C2×C379 | C2×C4 |
| LCS | G ▷ C379 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
1528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D379, #27131270, C2×C8×D379, … |
| maximal normal subgroup of | C16×D379, #27131270, C2×C8×D379, … |
| maximal quotient of | C8×Dic379, (C2×D379)⋊C8, Dic379⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6064, 21);