Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C193 ⋊ #108 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊#11715871 |
| commutator | C4×C193 | C2×C4 |
| Frattini | C4 | C2×#11715871 |
| Fitting | C8×C193 | C4 |
| socle | C2×C193 | C4⋊C4 |
| hypercenter | C8 | #11715871 |
| hypocenter | C193 | #108 |
| LCS | G ▷ C4×C193 ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,193|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^112,f^d=f^192398 conjugacy classes — view the full character table.
| maximal subgroup of | #27136177, #27136178, #27136183, … |
| maximal normal subgroup of | #27136177, #27136178, #27136183, … |
| maximal quotient of | #27136120, #27136123, #27136135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 216);