Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic193 |
| derived, Sylow | C193 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D193 |
| commutator, hypocenter | C193 | C23×C4 |
| Frattini | C2 | C23×D193 |
| Fitting, socle | C24×C193 | C2 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C24 | |
236 conjugacy classes of subgroups.
1568 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20259806, C22⋊C4×Dic193, #27135117, … |
| maximal normal subgroup of | C2×#20259806, C22⋊C4×Dic193, #27135117, … |
| maximal quotient of | C22×C4×Dic193, C22×C22⋊Dic193, C22×C4⋊Dic193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 181);