Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#14581702 |
| Sylow | C83 ⋊ C2×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D83 |
| commutator | C2×C83 | C2×C42 |
| Frattini | C2×C4 | C22×D83 |
| Fitting | C22×C8×C83 | C2 |
| socle | C23×C83 | C2×C4 |
| hypercenter | C22×C8 | D83 |
| hypocenter | C83 | C2×#97 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
146 conjugacy classes of subgroups.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #97×Dic83, C4×#14581702, #24907149, … |
| maximal normal subgroup of | #97×Dic83, C4×#14581702, #24907149, … |
| maximal quotient of | C4×#14581702, C2×#19127455, #24907208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 497);