Finite Group Databasebeta

C2×C5×(C2×D3)⋊Dic3 #13087228

order1440
isoclinismisoclinic class of #625
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC2×C5×(C2×D3)⋊Dic3

Splittings

HallC32×C5 ⋊ C2×C22⋊C4
SylowC32 ⋊ C2×C5×C22⋊C4

Subgroups

subgroupG/H
center, hypercenterC23×C5D32
commutatorC2×C32C22×C4×C5
FrattiniC22C2×C5×D32
Fitting, socleC23×C32×C5C22
prime radicalC23×C3×C5×D3C2
cosocleC22×C32C23×C5
hypocenterC32C2×C5×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C5

582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3545);