Finite Group Databasebeta

C2×#14271285 #16828388

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14271285

Splittings

SylowC29 ⋊ C2×#444

Subgroups

subgroupG/H
centerC2×C4D4×D29
commutatorC4×C29C23×C4
FrattiniC2×C4C23×D29
Fitting, prime radicalC2×C29×#135C2
socleC22×C29C4×D4
cosocleC2×C4×C29C24
hypercenterC2×#135D29
hypocenterC29C2×#444
LCSG ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13406);