Finite Group Databasebeta

C2×#20300906 #28411460

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

Aliases

direct productC2×#20300906

Splittings

SylowC229 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22#16814643
commutatorC22×C229C22×C4
FrattiniC2×C4C22×D229
FittingC2×M16×C229C2
socleC22×C229C22⋊C4
prime radicalC23×C229C2×C4
cosocleC2×C4×C229C23
hypercenterC2×M16D229
hypocenterC229C2×#101
LCSG ▷ C22×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

2302 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 528);