Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
| direct product | #97×Dic59 |
| Sylow | C59 ⋊ C4×#97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator | C2×C59 | C43 |
| Fitting | C2×#97×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C2×#97 | D59 |
| hypocenter | C59 | C4×#97 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
360 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479602, #329×Dic59, #28479606, … |
| maximal normal subgroup of | #28479602, #329×Dic59, #28479606, … |
| maximal quotient of | #322×Dic59, #97×C59⋊C8, #28478041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4193);