Finite Group Databasebeta

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C4×C5×C199⋊C3 #26045889

order11940
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C199⋊C3
unambiguous semidirect product(C4×C199)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C199)⋊C3

Splittings

Fitting, HallC4×C5×C199 ⋊ C3
derived, SylowC199 ⋊ C3×C4×C5
HallC5×C199 ⋊ C3×C4
HallC4×C199 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C199⋊C3
commutator, hypocenterC199C3×C4×C5
FrattiniC2C2×C5×C199⋊C3
FittingC4×C5×C199C3
socleC2×C5×C199C2×C3
prime radicalC2×C5×C199⋊C3C2
cosocleC2×C199C2×C3×C5
LCSG ▷ C199
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1380 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×#13184226, C5×Dic3×C199⋊C3, C3×C4×C5×C199⋊C3
maximal normal subgroup ofC4×C5×#13184226, C3×C4×C5×C199⋊C3
maximal quotient ofC4×C5×#13184224, C5×Dic3×C199⋊C3, C3×C4×C5×C199⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11940, 2);