Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C4⋊(C83⋊C8) |
| Sylow | C83 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35290931, #35290932, #35290946, … |
| maximal normal subgroup of | #35290931, #35290932, #35290946, … |
| maximal quotient of | C8×C4⋊(C83⋊C8), #35295529, #35295538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4359);