Finite Group DatabasebetaFinite Group Databasebeta| order | 7712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C241 ⋊ C2 |
| Sylow | C241 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D241 |
| commutator, socle | C2×C241 | C22×C4 |
| Frattini | C4 | C22×D241 |
| Fitting | C2×C8×C241 | C2 |
| hypercenter | C2×C8 | D241 |
| hypocenter | C241 | #131 |
| LCS | G ▷ C2×C241 ▷ C241 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,241|a^2=d,d^2=e,c^b=ce,f^c=f^2401940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507500, #29507502, #29507832, … |
| maximal normal subgroup of | #29507500, #29507502, #29507832, … |
| maximal quotient of | #29507671, #29507672, #29507682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7712, 152);