Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#41×D79 |
| Fitting | C22×#41×C79 ⋊ C2 |
| Sylow | C79 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D79 |
| commutator, cosocle | C2×C79 | C26 |
| Frattini | C2 | C25×D79 |
| Fitting | C22×#41×C79 | C2 |
| socle | C23×C79 | C24 |
| hypercenter | C22×#41 | D79 |
| hypocenter | C79 | C23×#41 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
6520 conjugacy classes of subgroups.
1640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1780×D79, #34287380, #34287384, … |
| maximal normal subgroup of | #1780×D79, #34287380, #34287384, … |
| maximal quotient of | C22×#117×D79, C22×C4×D4×D79, C22×C4×Q8×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19306);