Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C193 ⋊ C2 |
| Sylow | C193 ⋊ #392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D193 |
| commutator, socle, cosocle | C23×C193 | C23 |
| Fitting | C2×C22⋊C4×C193 | C2 |
| hypercenter | C2×C22⋊C4 | D193 |
| hypocenter | C193 | #392 |
| LCS | G ▷ C23×C193 ▷ C193 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
322 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,193|b^a=bd,c^a=ce,c^b=cf,g^b=g^192,g^c=g^1921942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 458);