Finite Group Databasebeta

C2×#14271033 #16821893

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14271033

Splittings

SylowC29 ⋊ C2×#384

Subgroups

subgroupG/H
centerC24C22×D29
commutatorC22×C29C23×C4
FrattiniC23C23×D29
FittingC22×C42×C29C2
socle, prime radicalC24×C29C23
cosocleC23×C29C24
hypercenterC22×C42D29
hypocenterC29C2×#384
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C24 ◁ C22×C42

888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6911);