Finite Group Databasebeta

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C4×C5×C11×C37⋊C3 #37567482

order24420
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C11×C37⋊C3
unambiguous semidirect product(C4×C37)⋊(C3×C5×C11)
unambiguous semidirect product(C4×C5×C37)⋊(C3×C11)
unambiguous semidirect product(C4×C5×C11×C37)⋊C3

Splittings

Fitting, HallC4×C5×C11×C37 ⋊ C3
derived, SylowC37 ⋊ C3×C4×C5×C11
HallC5×C11×C37 ⋊ C3×C4
HallC4×C11×C37 ⋊ C3×C5
HallC4×C5×C37 ⋊ C3×C11
HallC11×C37 ⋊ C3×C4×C5
HallC5×C37 ⋊ C3×C4×C11
HallC4×C37 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC4×C5×C11C37⋊C3
commutator, hypocenterC37C3×C4×C5×C11
FrattiniC2C2×C5×C11×C37⋊C3
FittingC4×C5×C11×C37C3
socleC2×C5×C11×C37C2×C3
prime radicalC2×C5×C11×C37⋊C3C2
cosocleC2×C37C2×C3×C5×C11
LCSG ▷ C37
UCSC1 ◁ C4×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8140

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 3);