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C4×C5×#11762245 #36343146

order21660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#11762245

Splittings

Fitting, HallC4×C5×C192 ⋊ C3
derived, SylowC192 ⋊ C3×C4×C5
HallC5×C192 ⋊ C3×C4
HallC4×C192 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5#11762245
commutator, hypocenterC192C3×C4×C5
FrattiniC2C2×C5×#11762245
FittingC4×C5×C192C3
socleC2×C5×C192C2×C3
prime radicalC2×C5×#11762245C2
cosocleC2×C192C2×C3×C5
LCSG ▷ C192
UCSC1 ◁ C4×C5

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7220

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21660, 70);