Finite Group DatabasebetaFinite Group Databasebeta| order | 8612 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2153 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2153 | C4 |
| LCS | G ▷ C2153 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,2153|a^2=b,c^a=c^232,c^b=c^2152542 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22575583, #31771881, C3×#22575583, … |
| maximal normal subgroup of | C2×#22575583, #31771881, C3×#22575583 |
| maximal quotient of | #31771879, C2×#22575583, C3×#22575583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8612, 3);