Finite Group Databasebeta

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C22×#91776 #14478842

order1920
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#91776

Splittings

HallC3×C5 ⋊ C22×C4×Q8
SylowC5 ⋊ C22×#887
SylowC3 ⋊ C22×#4033

Subgroups

subgroupG/H
centerC24C22×D15
commutatorC2×C3×C5C24×C4
FrattiniC22C24×D15
FittingC22×C3×C5×C4⋊C4C2
socle, prime radicalC24×C3×C5C23
cosocleC22×C3×C5C25
hypercenterC22×C4⋊C4D15
hypocenterC3×C5C22×C4×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C22×C4⋊C4

3328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 204540);