Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14581951 |
| Fitting | C22×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D167 |
| commutator, cosocle | C2×C167 | C25 |
| Frattini | C2 | C24×D167 |
| Fitting | C22×Q8×C167 | C2 |
| socle | C23×C167 | C23 |
| hypercenter | C22×Q8 | D167 |
| hypocenter | C167 | C22×#41 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
890 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324065, #36324077, #36326627, … |
| maximal normal subgroup of | #36324065, #36324077, #36326627, … |
| maximal quotient of | C22×#19128790, C22×#19128794, C22×Q8×Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1377);