Finite Group Databasebeta

C2×#20301049 #28412465

order14656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20301049

Splittings

SylowC229 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊#11745021
commutatorC22×C229C22×C4
FrattiniC22C22×#11745021
FittingC22×C4×C229C4
socleC22×C229C22⋊C4
prime radicalC23×C229C2×C4
cosocleC2×Dic229C23
hypercenterC22×C4#11745021
hypocenterC229C2×#101
LCSG ▷ C22×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 1533);