Finite Group Databasebeta

C2×C3×C4⋊Dic15 #13088022

order1440
isoclinismisoclinic class of Dic30
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×C4⋊Dic15

Splittings

HallC32×C5 ⋊ C2×C4⋊C4
SylowC32 ⋊ C2×C4⋊Dic5
SylowC5 ⋊ C2×C3×C4⋊Dic3

Subgroups

subgroupG/H
centerC23×C3C2×D15
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C22×C3×D15
FittingC22×C32×C4×C5C2
socle, prime radicalC23×C32×C5C22
cosocleC22×C3×C5C23×C3
hypercenterC22×C3×C4D15
hypocenterC3×C5C2×C3×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4339);