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C4⋊C4×#1220 #14327003

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×#1220

Splittings

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

Subgroups

subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×C4⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC22×C4⋊C4D15
hypocenterC3×C5D4×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4⋊C4

1552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

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, 52701);