Finite Group DatabasebetaFinite Group Databasebeta| order | 6368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#15691873 |
| Fitting | C2×Q8×C199 ⋊ C2 |
| Sylow | C199 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D199 |
| commutator | C4×C199 | C23 |
| Frattini | C4 | C22×D199 |
| Fitting | C2×Q8×C199 | C2 |
| socle | C22×C199 | D4 |
| hypercenter | C2×Q8 | D199 |
| hypocenter | C199 | C2×SD16 |
| LCS | G ▷ C4×C199 ▷ C2×C199 ▷ C199 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
1004 conjugacy classes — view the full character table.
| maximal subgroup of | #27164103, C4×#15691873, #27164116, … |
| maximal normal subgroup of | #27164103, C4×#15691873, #27164116, … |
| maximal quotient of | C2×#20263875, C2×#20263879, C2×#20263886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6368, 159);