Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C2×#120×D83 |
| Fitting | C2×#120×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D83 |
| commutator, cosocle | C22×C83 | C25 |
| Frattini | C22 | C24×D83 |
| Fitting | C2×#120×C83 | C2 |
| socle | C23×C83 | C24 |
| hypercenter | C2×#120 | D83 |
| hypocenter | C83 | C22×#120 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
4544 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 661 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319862, #1889×D83, #1898×D83, … |
| maximal normal subgroup of | #35319862, #1889×D83, #1898×D83, … |
| maximal quotient of | C2×#379×D83, C2×#385×D83, C2×#386×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17724);