Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×#11761628 |
| Fitting | C24×C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D67 |
| commutator | C2×C67 | C26 |
| Frattini | C2 | C25×D67 |
| Fitting | C24×C4×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C24×C4 | D67 |
| hypocenter | C67 | C23×#41 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C4 | |
6520 conjugacy classes of subgroups; only the 3301 normal subgroups are shown.
This group has 6520 conjugacy classes of subgroups — too many to draw. Only its 3301 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30777590, #30778347, #30778348, … |
| maximal normal subgroup of | #30777590, #30778347, #30778348, … |
| maximal quotient of | C23×#14524000, C23×#14524002, C23×C4×C22⋊D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 19308);