Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×Dic236 |
| Sylow | C59 ⋊ C8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | D236 |
| commutator | C4×C59 | C22×C8 |
| Frattini | C42 | C22×D59 |
| Fitting | C82×C59 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | C82 | D59 |
| hypocenter | C59 | C8×Q16 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475340, #28475342, #28475346, … |
| maximal normal subgroup of | #28475340, #28475342, #28475346, … |
| maximal quotient of | C8×#14273652, C8×#14273661, #28482610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3318);