Finite Group Databasebeta

C22×(C2×D487)⋊C4 #44529497

order31168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D487)⋊C4

Splittings

FittingC23×C4×C487 ⋊ C2
SylowC487 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D487
commutatorC2×C487C23×C4
FrattiniC22C23×D487
FittingC23×C4×C487C2
socleC24×C487C22
prime radicalC24×D487C2
cosocleC22×C487C24
hypercenterC23×C4D487
hypocenterC487C22×C22⋊C4
LCSG ▷ C2×C487 ▷ C487
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15584

Conjugacy classes & character table

7816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31168, 996);