Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| isoclinism | isoclinic class of C7⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C7⋊#595 |
| unambiguous semidirect product | C7⋊(C23×#595) |
| Fitting, socle, Hall | C7×C17×C23 ⋊ C4 |
| derived, Hall | C7×C17 ⋊ C4×C23 |
| Hall | C17×C23 ⋊ Dic7 |
| Hall | C7×C23 ⋊ #595 |
| Sylow | C17 ⋊ C23×Dic7 |
| Sylow | C7 ⋊ C23×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C7⋊#595 |
| commutator, hypocenter | C7×C17 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C23 | C4 |
| prime radical | C7×C23×D17 | C2 |
| cosocle | C7×D17 | C2×C23 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×ΓL(1,𝔽8)⋊#595, C3×C23×C7⋊#595, C23×C3⋊(C7⋊#595) |
| maximal normal subgroup of | C23×ΓL(1,𝔽8)⋊#595, C3×C23×C7⋊#595 |
| maximal quotient of | C3×C23×C7⋊#595, C23×C3⋊(C7⋊#595) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 14);