Finite Group Databasebeta

C2×#14272051 #16835692

order3712
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14272051

Splittings

SylowC29 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C4C2×#1181
commutatorC2×C29C2×C4×C8
FrattiniC2×C4C22×#1181
FittingC2×C42×C29C4
socle, prime radicalC23×C29C2×C8
cosocleC2×#6597C23
hypercenterC2×C42#1181
hypocenterC29C2×#346
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C2×C42

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 20710);