Finite Group Databasebeta

C2×#14271734 #16832806

order3712
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14271734

Splittings

SylowC29 ⋊ C2×#536

Subgroups

subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
Fitting, prime radicalC22×#41×C29C2
socleC23×C29C24
hypercenterC22×#41D29
hypocenterC29C2×#536
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×#41

1512 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, 17824);