Finite Group Databasebeta

C2×#20300905 #28411458

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

Aliases

direct productC2×#20300905

Splittings

SylowC229 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic229
commutatorC22×C229C22×C4
FrattiniC2×C4C22×D229
Fitting, prime radicalC22×D4×C229C2
socleC22×C229C22⋊C4
cosocleC2×C4×C229C23
hypercenterC22×D4D229
hypocenterC229C2×#100
LCSG ▷ C22×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3664

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, 526);