Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #383×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2852 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #383×C79 | C2 |
| prime radical | C22×D316 | C22 |
| hypercenter | #383 | D79 |
| hypocenter | C79 | #2852 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #383 | |
582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=ef,c^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^78,h^d=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34460932, #34460942, #34460963, … |
| maximal normal subgroup of | #34460932, #34460942, #34460963, … |
| maximal quotient of | #34219440, #34219492, #34219503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12826);