Finite Group Databasebeta

C2×#14270926 #16819206

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

Aliases

direct productC2×#14270926

Splittings

SylowC29 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24D116
commutatorC4×C29C2×C42
FrattiniC22×C4C22×D29
FittingC23×C8×C29C2
socle, prime radicalC24×C29D4
cosocleC22×C4×C29C23
hypercenterC23×C8D29
hypocenterC29C2×#340
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

512 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, 4224);