Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×C167⋊C16 |
| derived, Sylow | C167 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D167 |
| commutator, hypocenter | C167 | C22×C16 |
| Frattini | C8 | C22×D167 |
| Fitting | C22×C8×C167 | C2 |
| socle, prime radical | C23×C167 | C8 |
| cosocle | C8×C167 | C23 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C22×C8 | |
98 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322215, #36322216, #36322227, … |
| maximal normal subgroup of | #36322215, #36322216, #36322227, … |
| maximal quotient of | C2×C4×C167⋊C16, C2×C22⋊(C167⋊C16), C2×C4⋊(C167⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 961);