Finite Group Databasebeta

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C3×C11×#10625191 #37567575

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

Aliases

direct productC3×C11×#10625191

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3×C11#10625191
commutator, hypocenterC5×C37C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C37C4
prime radicalC3×C11×D185C2
cosocleD185C2×C3×C11
LCSG ▷ C5×C37
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 96);