Finite Group Databasebeta

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C22×C5×#825 #14412791

order1920
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC22×C5×#825

Splittings

FittingC22×C3×C5×M16 ⋊ C2
HallC3×C5 ⋊ C22×#104
SylowC3 ⋊ C22×C5×#104

Subgroups

subgroupG/H
centerC22×C4×C5#67
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC22×C3×C5×M16C2
socleC23×C3×C5C22⋊C4
prime radicalC22×C5×#235C2
cosocleC2×C3×C4C24×C5
hypercenterC22×C5×M16D3
hypocenterC3C22×C5×#104
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C23×C4×C5 ◁ C22×C5×M16

1712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138489);