Finite Group DatabasebetaFinite Group Databasebeta| order | 6176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic386 |
| Sylow | C193 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D193 |
| commutator | C2×C193 | C24 |
| Frattini | C2 | C23×D193 |
| Fitting | C22×C4×C193 | C2 |
| socle | C23×C193 | C22 |
| hypercenter | C22×C4 | D193 |
| hypocenter | C193 | C22×Q8 |
| LCS | G ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
156 conjugacy classes of subgroups.
1556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27135163, #27135164, #27135165, … |
| maximal normal subgroup of | #27135163, #27135164, #27135165, … |
| maximal quotient of | C22×#15690534, C22×C4⋊Dic193, C2×C4×Dic386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6176, 186);