Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D83 |
| commutator | C2×C83 | C22×C8 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | C4×C8×C83 | C2 |
| socle | C22×C83 | C22×C4 |
| hypercenter | C4×C8 | D83 |
| hypocenter | C83 | #431 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^821352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #431×D83, C2×#19127752, #24916091, … |
| maximal normal subgroup of | #431×D83, C2×#19127752, #24916091, … |
| maximal quotient of | #24907208, C4×(C2×D83)⋊C8, C4×Dic83⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 600);