Finite Group Databasebeta

C2×#14270923 #16819198

order3712
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14270923

Splittings

SylowC29 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4D116
commutatorC4×C29C2×C42
FrattiniC22×C4C22×D29
FittingC22×C42×C29C2
socleC23×C29C22⋊C4
prime radicalC24×C29D4
cosocleC22×C4×C29C23
hypercenterC22×C42D29
hypocenterC29C2×#339
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 4216);