Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#15690545 |
| Sylow | C193 ⋊ C2×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D193 |
| commutator | C4×C193 | C23 |
| Frattini | C4 | C22×D193 |
| Fitting | C2×Q8×C193 | C2 |
| socle | C22×C193 | D4 |
| hypercenter | C2×Q8 | D193 |
| hypocenter | C193 | C2×Q16 |
| LCS | G ▷ C4×C193 ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
60 conjugacy classes of subgroups.
974 conjugacy classes — view the full character table.
| maximal subgroup of | #27135351, C4×#15690545, #27135363, … |
| maximal normal subgroup of | #27135351, C4×#15690545, #27135363, … |
| maximal quotient of | C2×#20259822, C2×#20259823, C2×#20259832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 163);