Finite Group Databasebeta

C2×#14270997 #16821784

order3712
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14270997

Splittings

SylowC29 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D29
commutatorC2×C29C22×C16
FrattiniC16C22×D29
FittingC22×C16×C29C2
socleC22×C29C2×C16
prime radicalC23×C29C16
cosocleC16×C29C23
hypercenterC22×C16D29
hypocenterC29C2×M64
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C16 ◁ C22×C16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6802);