Finite Group Databasebeta

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C22×#91093 #14412246

order1920
isoclinismisoclinic class of #6715
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#91093

Splittings

FittingC22×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ C22×#102
SylowC5 ⋊ C22×#809
SylowC3 ⋊ C22×#3941

Subgroups

subgroupG/H
centerC24#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5D4
prime radicalC23×D60C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C4⋊C4D15
hypocenterC3×C5C22×#102
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

2144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137944);