Finite Group Databasebeta

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C5×C11×Dic37⋊C3 #37567506

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

Aliases

direct productC5×C11×Dic37⋊C3
unambiguous semidirect productDic37⋊(C3×C5×C11)
unambiguous semidirect product(C5×Dic37)⋊(C3×C11)
unambiguous semidirect product(C5×C11×Dic37)⋊C3

Splittings

derived, SylowC37 ⋊ C3×C4×C5×C11
HallC5×C11×Dic37 ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C4
HallC5×C11×C37 ⋊ C3×C4
HallC11×Dic37 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C4×C5
HallC5×Dic37 ⋊ C3×C11
HallC5×C37⋊C3 ⋊ C4×C11
HallC11×C37 ⋊ C3×C4×C5
HallC5×C37 ⋊ C3×C4×C11
HallDic37 ⋊ C3×C5×C11
HallC37⋊C3 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D37⋊C3
commutator, hypocenterC37C3×C4×C5×C11
FrattiniC2C5×C11×D37⋊C3
Fitting, socleC2×C5×C11×C37C2×C3
prime radicalC2×C5×C11×C37⋊C3C2
cosocleC2×C37C2×C3×C5×C11
LCSG ▷ C37
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8140

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 27);