Finite Group Databasebeta

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C4×C5×C523⋊C3 #44535923

order31380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C523⋊C3
unambiguous semidirect product(C4×C523)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C523)⋊C3

Splittings

Fitting, HallC4×C5×C523 ⋊ C3
derived, SylowC523 ⋊ C3×C4×C5
HallC5×C523 ⋊ C3×C4
HallC4×C523 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C523⋊C3
commutator, hypocenterC523C3×C4×C5
FrattiniC2C2×C5×C523⋊C3
FittingC4×C5×C523C3
socleC2×C5×C523C2×C3
prime radicalC2×C5×C523⋊C3C2
cosocleC2×C523C2×C3×C5
LCSG ▷ C523
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10460

Conjugacy classes & character table

3540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31380, 2);