Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C4×C167⋊C16 |
| derived, Sylow | C167 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D167 |
| commutator, hypocenter | C167 | C4×C16 |
| Frattini | C2×C8 | C2×D167 |
| Fitting | C4×C8×C167 | C2 |
| socle, prime radical | C22×C167 | C2×C8 |
| cosocle | C2×C8×C167 | C22 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C4×C8 | |
58 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C167⋊C8, C8×C167⋊C16, #36322054, … |
| maximal normal subgroup of | C16×C167⋊C8, C8×C167⋊C16, #36322054, … |
| maximal quotient of | C8×C167⋊C16, #36322056, #36322216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 323);