Finite Group DatabasebetaFinite Group Databasebeta| order | 8652 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#14524189 |
| Fitting, Hall | C4×C7×C103 ⋊ C3 |
| derived, Hall | C7×C103 ⋊ C3×C4 |
| Hall | C4×C103 ⋊ ΓL(1,𝔽8) |
| Sylow | C103 ⋊ C4×ΓL(1,𝔽8) |
| Hall | C4×C7 ⋊ C103⋊C3 |
| Sylow | C7 ⋊ C4×C103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14524189 |
| commutator, hypocenter | C7×C103 | C3×C4 |
| Frattini | C2 | C2×#14524189 |
| Fitting | C4×C7×C103 | C3 |
| socle | C2×C7×C103 | C2×C3 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
972 conjugacy classes — view the full character table.
| maximal subgroup of | C4×ΓL(1,𝔽8)×C103⋊C3, Dic3×#14524189, C3×C4×#14524189 |
| maximal normal subgroup of | C4×ΓL(1,𝔽8)×C103⋊C3, C3×C4×#14524189 |
| maximal quotient of | C4×#20266515, Dic3×#14524189, C3×C4×#14524189 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8652, 5);