Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C193 ⋊ C2 |
| Sylow | C193 ⋊ #137 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D193 |
| commutator | C4×C193 | C23 |
| Frattini | C4 | C22×D193 |
| Fitting | SD16×C193 | C2 |
| socle | C2×C193 | C2×D4 |
| hypercenter | SD16 | D193 |
| hypocenter | C193 | #137 |
| LCS | G ▷ C4×C193 ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,193|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^c=f^192683 conjugacy classes — view the full character table.
| maximal subgroup of | #137×D193, C2×#20259928, #27136055, … |
| maximal normal subgroup of | #137×D193, C2×#20259928, #27136055, … |
| maximal quotient of | #27135257, #27135266, #27135298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 175);