Finite Group Databasebeta

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C4×C4⋊(3−1+2⋊C4) #13142440

order1728
isoclinismisoclinic class of 3−1+2⋊Q8
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊(3−1+2⋊C4)
unambiguous semidirect product(C4×C4⋊Dic9)⋊C3

Splittings

Sylow3−1+2 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×AGL(1,ℤ/9)
commutatorC2×C9C2×C3×C42
Frattini, socleC23×C3C22×C3×D3
FittingC2×C42×3−1+2C2
prime radicalC23×C32C22×D3
cosocleC23×C9C23×C3
hypercenterC2×C42AGL(1,ℤ/9)
hypocenterC9C3×C4×C4⋊C4
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C42

636 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8503);