Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#19099398 |
| Fitting | C2×H(5,𝔽2)×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D79 |
| commutator, cosocle | C2×C79 | C26 |
| Frattini | C2 | C25×D79 |
| Fitting | C2×H(5,𝔽2)×C79 | C2 |
| socle | C22×C79 | C25 |
| hypercenter | C2×H(5,𝔽2) | D79 |
| hypocenter | C79 | C2×#585 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34287530, #34287538, #34287562, … |
| maximal normal subgroup of | #34287530, #34287538, #34287562, … |
| maximal quotient of | C2×#23776598, C2×#23776600, C2×#23776604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19317);