Finite Group Databasebeta

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C11×C3⋊#10625191 #37567599

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

Aliases

direct productC11×C3⋊#10625191
unambiguous semidirect productC3⋊(C11×#10625191)

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C4
derived, HallC3×C5×C37 ⋊ C4×C11
HallC5×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ AGL(1,𝔽5)
HallC11×C37 ⋊ ΓL(1,𝔽16)
HallC5×C37 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ #3866
HallC3×C37 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C3⋊#3866
SylowC37 ⋊ C11×ΓL(1,𝔽16)
HallC3×C11 ⋊ #10625191
HallC3×C5 ⋊ C11×#3866
SylowC5 ⋊ C11×C3⋊#3866
SylowC3 ⋊ C11×#10625191

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#10625191
commutator, hypocenterC3×C5×C37C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C37C4
prime radicalC3×C11×D185C2
cosocleC3×D185C2×C11
LCSG ▷ C3×C5×C37
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

1584 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 120);