Finite Group Databasebeta

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C11⋊C5×#3866⋊C3 #37567519

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

Aliases

direct productC11⋊C5×#3866⋊C3
unambiguous semidirect product#3866⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×#3866⋊C3)⋊C5
unambiguous semidirect product(C11⋊C5×#3866)⋊C3

Splittings

Fitting, socle, derived, HallC11×C37 ⋊ C3×C4×C5
HallC11⋊C5×#3866 ⋊ C3
HallC11⋊C5×C37⋊C3 ⋊ C4
HallC11×#3866⋊C3 ⋊ C5
HallC37×C11⋊C5 ⋊ C3×C4
HallC11×#3866 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C4×C5
Hall#3866 ⋊ C3×C11⋊C5
HallC37⋊C3 ⋊ C4×C11⋊C5
SylowC37 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C5×#3866⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC11×C37C3×C4×C5
prime radicalC11⋊C5×D37⋊C3C2
cosocleC11×D37C2×C3×C5
LCSG ▷ C11×C37
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 407

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 40);