Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D412 |
| Fitting | C4×Q8×C103 ⋊ C2 |
| Sylow | C103 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D103 |
| commutator, socle | C22×C103 | C24 |
| Fitting | C4×Q8×C103 | C2 |
| hypercenter | C4×Q8 | D103 |
| hypocenter | C103 | D4×Q8 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
280 conjugacy classes of subgroups.
1045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27194245, #27194249, #27194307, … |
| maximal normal subgroup of | #27194245, #27194249, #27194307, … |
| maximal quotient of | Q8×(C2×D103)⋊C4, C4⋊C4×D412, Q8×C4⋊Dic103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1216);