Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C2×#124×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2610 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | C2×#124×C79 | C2 |
| prime radical | #19098471 | C2 |
| hypercenter | C2×#124 | D79 |
| hypocenter | C79 | #2610 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
576 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=f,b^2=eg,d^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=cg,h^c=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34185601, #34185611, #34262509, … |
| maximal normal subgroup of | #34185601, #34185611, #34262509, … |
| maximal quotient of | #34210968, #34211013, #34212347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10199);