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C22⋊C4×#1220 #14325903

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×#1220

Splittings

FittingC22×C3×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ D4×C22⋊C4
SylowC5 ⋊ C22⋊C4×#67
SylowC3 ⋊ C22⋊C4×C22⋊D5

Subgroups

subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×C22⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC23×#1220C2
hypercenterC22×C22⋊C4D15
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C22⋊C4

2504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51601);