Finite Group Databasebeta

C4×#16814645 #28411334

order14656
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16814645

Splittings

SylowC229 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D229
commutatorC2×C229C2×C42
FrattiniC23C22×D229
FittingC2×C42×C229C2
socle, prime radical, cosocleC23×C229C23
hypercenterC2×C42D229
hypocenterC229C4×C4⋊C4
LCSG ▷ C2×C229 ▷ C229
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14656

Conjugacy classes & character table

3688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 402);