Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#11715871 |
| Fitting | C8×C193 ⋊ C4 |
| derived, Sylow | C193 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #11715871 |
| commutator, hypocenter | C193 | C4×C8 |
| Frattini | C4 | C2×#11715871 |
| Fitting | C8×C193 | C4 |
| socle | C2×C193 | C42 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
416 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11715871, #27136146, C2×C8×#11715871, … |
| maximal normal subgroup of | C16×#11715871, #27136146, C2×C8×#11715871, … |
| maximal quotient of | C8×#13095400, #27136101, #27136124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 198);