Finite Group Databasebeta

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C22×C3×D5×C4⋊C4 #14478701

order1920
automorphism?
homologyAbelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×C3×D5×C4⋊C4

Splittings

FittingC22×C3×C5×C4⋊C4 ⋊ C2
HallC3×C5 ⋊ C23×C4⋊C4
SylowC5 ⋊ C23×C3×C4⋊C4

Subgroups

subgroupG/H
centerC24×C3C22×D5
commutatorC2×C5C24×C3×C4
FrattiniC22C24×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5C23
prime radicalC24×C3×D5C22
cosocleC22×C5C25×C3
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C23×C3×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

4976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 204399);