Finite Group Databasebeta

C2×#14271159 #16827988

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

Aliases

direct productC2×#14271159

Splittings

SylowC29 ⋊ C2×#416

Subgroups

subgroupG/H
centerC22×C4C22⋊D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
Fitting, prime radicalC22×#41×C29C2
socleC23×C29C2×D4
cosocleC2×C4×C29C24
hypercenterC22×#41D29
hypocenterC29C2×#416
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13006);