Finite Group Databasebeta

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Dic3×C37×C11⋊C5 #37567502

order24420
automorphism?
homologyAbelianization (H1) = C4×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C37×C11⋊C5
unambiguous semidirect productC3⋊(C4×C37×C11⋊C5)
unambiguous semidirect product(C11×Dic3)⋊(C5×C37)
unambiguous semidirect product(C11×Dic3×C37)⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C5×C37
HallC3×C37×C11⋊C5 ⋊ C4
HallC11×Dic3×C37 ⋊ C5
HallC3×C11×C37 ⋊ C4×C5
HallC11×C37 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ C4×C37
HallC11×Dic3 ⋊ C5×C37
HallC3×C37 ⋊ C4×C11⋊C5
SylowC11 ⋊ C5×Dic3×C37
SylowC3 ⋊ C4×C37×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C37D3×C11⋊C5
commutator, hypocenterC3×C11C4×C5×C37
FrattiniC2D3×C37×C11⋊C5
Fitting, socleC2×C3×C11×C37C2×C5
prime radicalC2×C3×C37×C11⋊C5C2
cosocleC2×C3×C11C2×C5×C37
LCSG ▷ C3×C11
UCSC1 ◁ C2×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4884

Conjugacy classes & character table

1554 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 23);