Finite Group Databasebeta

C2×#14270929 #16819221

order3712
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14270929

Splittings

SylowC29 ⋊ C2×#342

Subgroups

subgroupG/H
centerC23#90781
commutatorC22×C29C2×C42
FrattiniC24C22×D29
FittingC22×C22⋊C4×C29C2
socleC23×C29C22⋊C4
prime radicalC25×C29C22
cosocleC24×C29C23
hypercenterC22×C22⋊C4D29
hypocenterC29C2×#342
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 4239);