Finite Group Databasebeta

C2×#14271091 #16822719

order3712
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14271091

Splittings

SylowC29 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D29
commutator, cosocleC23×C29C24
FrattiniC23C23×D29
FittingC22×C22⋊C4×C29C2
socleC24×C29C23
prime radicalC25×C29C22
hypercenterC22×C22⋊C4D29
hypocenterC29C2×#397
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

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, 7737);