Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D113 |
| commutator, socle | C23×C113 | C23 |
| Fitting | C2×C4⋊C4×C113 | C2 |
| hypercenter | C2×C4⋊C4 | D113 |
| hypocenter | C113 | #398 |
| LCS | G ▷ C23×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^1121142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389568, #28389570, #28389575, … |
| maximal normal subgroup of | #28389568, #28389570, #28389575, … |
| maximal quotient of | #28388824, #28388825, #28388829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 480);