Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D167 |
| Fitting | H(5,𝔽2)×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D167 |
| commutator, socle, cosocle | C2×C167 | C25 |
| Fitting | H(5,𝔽2)×C167 | C2 |
| hypercenter | H(5,𝔽2) | D167 |
| hypocenter | C167 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
1445 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×D167, #455×D167, #36333492, … |
| maximal normal subgroup of | #453×D167, #455×D167, #36333492, … |
| maximal quotient of | #518×D167, #520×D167, #36337342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1378);