Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic83 |
| derived, Sylow | C83 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D83 |
| commutator, hypocenter | C83 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | C22×C8×C83 | C2 |
| socle | C23×C83 | C2×C4 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
1376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×Dic83, #97×Dic83, #24907149, … |
| maximal normal subgroup of | C4×C8×Dic83, #97×Dic83, #24907149, … |
| maximal quotient of | C4×C8×Dic83, C2×#19127455, #24907208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 494);