Finite Group Databasebeta

C2×#14271035 #16821902

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14271035

Splittings

SylowC29 ⋊ C2×#385

Subgroups

subgroupG/H
centerC24C22×D29
commutatorC22×C29C23×C4
FrattiniC23C23×D29
FittingC22×C22⋊C4×C29C2
socleC24×C29C23
prime radicalC25×C29C22
cosocleC23×C29C24
hypercenterC22×C22⋊C4D29
hypocenterC29C2×#385
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1232 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, 6920);