Finite Group DatabasebetaFinite Group Databasebeta| order | 16672 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#14523438 |
| Fitting | C8×C521 ⋊ C4 |
| derived, Sylow | C521 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14523438 |
| commutator, hypocenter | C521 | C4×C8 |
| Frattini | C4 | C2×#14523438 |
| Fitting | C8×C521 | C4 |
| socle | C2×C521 | C42 |
| prime radical | C2×D521 | C2×C4 |
| cosocle | C4×D521 | C22 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4168 |
1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#14523438, #45688319, C2×C8×#14523438, … |
| maximal normal subgroup of | C16×#14523438, #45688319, C2×C8×#14523438, … |
| maximal quotient of | C8×#16861967, #45688274, #45688297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16672, 198);