Finite Group DatabasebetaFinite Group Databasebeta| order | 6128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C383 ⋊ C2 |
| Sylow | C383 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D383 |
| commutator, socle | C2×C383 | C23 |
| Fitting | Q8×C383 | C2 |
| hypercenter | Q8 | D383 |
| hypocenter | C383 | #41 |
| LCS | G ▷ C2×C383 ▷ C383 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,383|c^2=d,b^a=bd,e^a=e^382,e^b=e^382,e^c=e^382965 conjugacy classes — view the full character table.
| maximal subgroup of | #27133862, #27133864, #27133868, … |
| maximal normal subgroup of | #27133862, #27133864, #27133868, … |
| maximal quotient of | #27133799, #27133803, Q8×Dic383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6128, 41);