Finite Group Databasebeta

C2×#14271147 #16827967

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14271147

Splittings

SylowC29 ⋊ C2×#413

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic29
commutatorC22×C29C23×C4
FrattiniC2×C4C23×D29
Fitting, prime radicalC22×#41×C29C2
socleC22×C29C2×C22⋊C4
cosocleC2×C4×C29C24
hypercenterC22×#41D29
hypocenterC29C2×#413
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 12985);