Finite Group DatabasebetaFinite Group Databasebeta| order | 6368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C199 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D199 |
| commutator, socle | C22×C199 | C23 |
| Fitting | C2×Q8×C199 | C2 |
| hypercenter | C2×Q8 | D199 |
| hypocenter | C199 | C4⋊Q8 |
| LCS | G ▷ C22×C199 ▷ C199 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,199|a^2=d,b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^1981004 conjugacy classes — view the full character table.
| maximal subgroup of | #27163816, #27164199, #27164201, … |
| maximal normal subgroup of | #27163816, #27164199, #27164201, … |
| maximal quotient of | #27163887, #27163913, #27163923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6368, 144);