Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C193 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #11715871 |
| commutator, hypocenter | C193 | C2×C16 |
| Frattini | C4 | C2×#11715871 |
| Fitting | C8×C193 | C4 |
| socle | C2×C193 | C2×C8 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,193|a^2=c,c^2=d,d^2=e,f^a=f^112,f^b=f^192,f^c=f^192416 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11715871, #27136146, #27136171, … |
| maximal normal subgroup of | C16×#11715871, #27136146, #27136171, … |
| maximal quotient of | #27136145, #27136154, #27136180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 219);