Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #548×D83 |
| Fitting | #548×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#548 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | #548×C83 | C2 |
| hypercenter | #548 | D83 |
| hypocenter | C83 | C2×#548 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ #548 | |
1620 conjugacy classes of subgroups.
1075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3265×D83, #3269×D83, #3270×D83, … |
| maximal normal subgroup of | #3265×D83, #3269×D83, #3270×D83, … |
| maximal quotient of | Q8×C22⋊C4×D83, #2341×D83, #2351×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17972);