Finite Group Databasebeta

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C11×#10625191⋊C3 #37567540

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

Aliases

direct productC11×#10625191⋊C3
unambiguous semidirect product#10625191⋊(C3×C11)
unambiguous semidirect product(C11×#10625191)⋊C3

Splittings

Fitting, socle, HallC5×C11×C37 ⋊ C3×C4
derived, HallC5×C37 ⋊ C3×C4×C11
HallC11×#10625191 ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C4
HallC11×C37⋊C3 ⋊ AGL(1,𝔽5)
Hall#10625191 ⋊ C3×C11
HallC5×C37⋊C3 ⋊ C4×C11
HallC11×C37 ⋊ C3×AGL(1,𝔽5)
HallC37⋊C3 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ #3866⋊C3
SylowC37 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×#3866⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#10625191⋊C3
commutator, hypocenterC5×C37C3×C4×C11
FrattiniC1G
Fitting, socleC5×C11×C37C3×C4
prime radicalC11×C5⋊(D37⋊C3)C2
cosocleD185C2×C3×C11
LCSG ▷ C5×C37
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2035

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 61);