Finite Group Databasebeta

C2×#14270939 #16821082

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

Aliases

direct productC2×#14270939

Splittings

SylowC29 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D29
commutatorC2×C29C2×C4×C8
FrattiniC2×C8C22×D29
FittingC2×C4×C8×C29C2
socle, prime radicalC23×C29C2×C8
cosocleC2×C8×C29C23
hypercenterC2×C4×C8D29
hypocenterC29C2×#346
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

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, 6100);