Finite Group Databasebeta

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C4×#11762245⋊C5 #36343120

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

Aliases

direct productC4×#11762245⋊C5
unambiguous semidirect product(C4×#11762245)⋊C5
unambiguous semidirect product(C4×C192⋊C5)⋊C3

Splittings

Fitting, HallC4×C192 ⋊ C3×C5
derived, SylowC192 ⋊ C3×C4×C5
HallC4×C192⋊C5 ⋊ C3
HallC4×#11762245 ⋊ C5
HallC192⋊C5 ⋊ C3×C4
Hall#11762245 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4#11762245⋊C5
commutator, hypocenterC192C3×C4×C5
FrattiniC2C2×#11762245⋊C5
FittingC4×C192C3×C5
socle, cosocleC2×C192C2×C3×C5
prime radicalC2×#11762245⋊C5C2
LCSG ▷ C192
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 380

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21660, 44);