Finite Group Databasebeta

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C4×#3675⋊C3 #13142808

order1728
isoclinismisoclinic class of #3672⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×#3675⋊C3
unambiguous semidirect product(C4×#3675)⋊C3

Splittings

FittingC4×Q8×3−1+2 ⋊ C2
Sylow3−1+2 ⋊ C4×SD16

Subgroups

subgroupG/H
centerC2×C4#611⋊C3
commutatorC4×C9C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingC4×Q8×3−1+2C2
socleC22×C3C2×C3×#67
prime radicalC2×C4⋊AGL(1,ℤ/9)C22
cosocleC2×C4×C9C23×C3
hypercenterC4×Q8AGL(1,ℤ/9)
hypocenterC9C3×C4×SD16
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

401 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8871);