Finite Group Databasebeta

C2×#20301055 #28412483

order14656
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20301055

Splittings

SylowC229 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC23C2×#11745021
commutatorC2×C229C22×C8
FrattiniC22C22×#11745021
FittingC22×C4×C229C4
socle, prime radicalC23×C229C2×C4
cosocleC2×Dic229C23
hypercenterC22×C4#11745021
hypocenterC229C2×C4⋊C8
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C23 ◁ C22×C4

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14656

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(14656, 1551);