Finite Group Databasebeta

C2×#20300995 #28412244

order14656
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20300995

Splittings

SylowC229 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D229
commutatorC2×C229C23×C4
FrattiniC4C23×D229
Fitting, prime radicalC2×#41×C229C2
socleC22×C229C22×C4
cosocleC4×C229C24
hypercenterC2×#41D229
hypocenterC229C2×#131
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1312);