Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C167⋊C8 |
| derived, Sylow | C167 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D167 |
| commutator, hypocenter | C167 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D167 |
| Fitting | C2×C42×C167 | C2 |
| socle, prime radical | C23×C167 | C2×C4 |
| cosocle | C2×C4×C167 | C23 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C167⋊#1273, #36321972, #36321974, … |
| maximal normal subgroup of | C167⋊#1273, #36321972, #36321974, … |
| maximal quotient of | C2×C8×C167⋊C8, C2×#24922990, M16×C167⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 495);