Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C193 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D193 |
| commutator, socle | C22×C193 | C23 |
| Fitting | C22×C4×C193 | C2 |
| hypercenter | C22×C4 | D193 |
| hypocenter | C193 | C22⋊Q8 |
| LCS | G ▷ C22×C193 ▷ C193 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,193|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^1921550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27134995, #27134997, #27135410, … |
| maximal normal subgroup of | #27134995, #27134997, #27135410, … |
| maximal quotient of | #27135119, #27135132, #27135143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 125);