Finite Group Databasebeta

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C4×C5×C379⋊C3 #36384397

order22740
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C379⋊C3
unambiguous semidirect product(C4×C379)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C379)⋊C3

Splittings

Fitting, HallC4×C5×C379 ⋊ C3
derived, SylowC379 ⋊ C3×C4×C5
HallC5×C379 ⋊ C3×C4
HallC4×C379 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C379⋊C3
commutator, hypocenterC379C3×C4×C5
FrattiniC2C2×C5×C379⋊C3
FittingC4×C5×C379C3
socleC2×C5×C379C2×C3
prime radicalC2×C5×C379⋊C3C2
cosocleC2×C379C2×C3×C5
LCSG ▷ C379
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7580

Conjugacy classes & character table

2580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22740, 2);