Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D83 |
| commutator | C2×C83 | C2×C42 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | C22×C8×C83 | C2 |
| socle | C22×C83 | C22×C4 |
| hypercenter | C22×C8 | D83 |
| hypocenter | C83 | #405 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=e,d^2=f,c^b=cf,g^b=g^821352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #24907218, #24907263, #24907264, … |
| maximal normal subgroup of | #24907218, #24907263, #24907264, … |
| maximal quotient of | #24907149, #24907159, #24907214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 504);