Finite Group Databasebeta

C2×#14271127 #16827928

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14271127

Splittings

SylowC29 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D29
commutatorC22×C29C23×C4
FrattiniC2×C4C23×D29
FittingC24×C4×C29C2
socleC23×C29C22×C4
prime radicalC25×C29C4
cosocleC2×C4×C29C24
hypercenterC24×C4D29
hypocenterC29C2×#407
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C24×C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

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, 12946);