Finite Group Databasebeta

C2×#14270924 #16819199

order3712
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14270924

Splittings

SylowC29 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4C22⋊D29
commutatorC4×C29C2×C42
FrattiniC22×C4C22×D29
FittingC22×M16×C29C2
socleC23×C29C22⋊C4
prime radicalC24×C29D4
cosocleC22×C4×C29C23
hypercenterC22×M16D29
hypocenterC29C2×#339
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

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, 4217);