Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#13050591 |
| Fitting | Q82×C83 ⋊ C2 |
| Sylow | C83 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D83 |
| commutator, socle, cosocle | C22×C83 | C25 |
| Fitting | Q82×C83 | C2 |
| prime radical | C2×#13050591 | C22 |
| hypercenter | Q82 | D83 |
| hypocenter | C83 | Q8×#41 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1068 conjugacy classes of subgroups; only the 529 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 529 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1075 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35380379, #35380387, #35380394, … |
| maximal normal subgroup of | #35380379, #35380387, #35380394, … |
| maximal quotient of | C4⋊C4×#13050591, Q8×#14581750, #35564060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18093);