Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C24×Dic166 |
| Sylow | C83 ⋊ C24×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D83 |
| commutator, cosocle | C2×C83 | C26 |
| Frattini | C2 | C25×D83 |
| Fitting | C24×C4×C83 | C2 |
| socle, prime radical | C25×C83 | C22 |
| hypercenter | C24×C4 | D83 |
| hypocenter | C83 | C24×Q8 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
6264 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24905733, #35326789, #35326790, … |
| maximal normal subgroup of | C2×#24905733, #35326789, #35326790, … |
| maximal quotient of | C24×Dic83⋊C4, C24×C4⋊Dic83, C23×C4×Dic166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19305);