Finite Group DatabasebetaFinite Group Databasebeta| order | 6368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C199 ⋊ C2 |
| Sylow | C199 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D199 |
| commutator, socle | C22×C199 | C23 |
| Fitting | C4⋊C4×C199 | C2 |
| hypercenter | C4⋊C4 | D199 |
| hypocenter | C199 | #123 |
| LCS | G ▷ C22×C199 ▷ C199 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,199|c^2=d,b^a=bd,c^a=ce,f^a=f^198,f^b=f^1981004 conjugacy classes — view the full character table.
| maximal subgroup of | #123×D199, C2×#20263940, #27164527, … |
| maximal normal subgroup of | #123×D199, C2×#20263940, #27164527, … |
| maximal quotient of | #27163880, #27163889, #27163896, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6368, 131);