Finite Group Databasebeta

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C3×C3⋊(C11⋊#63120) #38788197

order25740
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(C11⋊#63120)
unambiguous semidirect productC3⋊(C3×C11⋊#63120)
unambiguous semidirect productC11⋊(C3×C3⋊#63120)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derivedC3×C5×C11×C13 ⋊ C3×C4
HallC32×C11×C13 ⋊ AGL(1,𝔽5)
HallC5×C11×C13 ⋊ C3×Dic3
HallC32×C5×C13 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ C3×ΓL(1,𝔽16)
HallC32×C13 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ #63120
HallC5×C13 ⋊ C3×Dic33
HallC5×C11 ⋊ C3×Dic39
HallC32×C5 ⋊ Dic143
SylowC13 ⋊ C3×C3⋊(C11⋊AGL(1,𝔽5))
SylowC11 ⋊ C3×C3⋊#63120
SylowC32 ⋊ C11⋊#63120
SylowC5 ⋊ C3×Dic429

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C11⋊#63120)
commutator, hypocenterC3×C5×C11×C13C3×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×D5×C11×C13C2
cosocleC3×D5×C11×C13C2×C3
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C3

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4290

Conjugacy classes & character table

2583 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 428);