Finite Group DatabasebetaFinite Group Databasebeta| order | 17178 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#22575222 |
| Fitting, socle, Hall | C2×C7×C409 ⋊ C3 |
| derived, Hall | C7×C409 ⋊ C2×C3 |
| Hall | C2×C409 ⋊ ΓL(1,𝔽8) |
| Sylow | C409 ⋊ C2×ΓL(1,𝔽8) |
| Hall | C2×C7 ⋊ C409⋊C3 |
| Sylow | C7 ⋊ C2×C409⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22575222 |
| commutator, cosocle, hypocenter | C7×C409 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C409 | C3 |
| LCS | G ▷ C7×C409 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5726 |
1914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22575222, #46805266, #46805270, … |
| maximal normal subgroup of | C4×#22575222, #46805266, #46805270, … |
| maximal quotient of | C4×#22575222, C22×#22575222 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17178, 4);