Finite Group DatabasebetaFinite Group Databasebeta| order | 5648 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic353 |
| derived, Sylow | C353 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D353 |
| commutator, hypocenter | C353 | C22×C4 |
| Frattini | C2 | C22×D353 |
| Fitting, socle | C23×C353 | C2 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26014899, C2×C4×Dic353, C2×#19150714, … |
| maximal normal subgroup of | #26014899, C2×C4×Dic353, C2×#19150714, … |
| maximal quotient of | C2×C4×Dic353, C2×C22⋊Dic353, C2×C4⋊Dic353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5648, 33);