Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C23⋊#595) |
| unambiguous semidirect product | C23⋊(C7⋊#595) |
| Fitting, socle, derived, Hall | C7×C17×C23 ⋊ C4 |
| Hall | C17×C23 ⋊ Dic7 |
| Hall | C7×C23 ⋊ #595 |
| Hall | C7×C17 ⋊ Dic23 |
| Sylow | C23 ⋊ C7⋊#595 |
| Sylow | C17 ⋊ Dic161 |
| Sylow | C7 ⋊ C23⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C17×C23 | C4 |
| prime radical, cosocle | C7×C23×D17 | C2 |
| LCS | G ▷ C7×C17×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,17,23|a^2=b,c^a=c^6,d^a=d^13,e^a=e^22,d^b=d^16808 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊(C23⋊#595), C3×C7⋊(C23⋊#595), C3⋊(C7⋊(C23⋊#595)) |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊(C23⋊#595), C3×C7⋊(C23⋊#595) |
| maximal quotient of | C3×C7⋊(C23⋊#595), C3⋊(C7⋊(C23⋊#595)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 15);