Finite Group Databasebeta

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C7×C3⋊(C7⋊(Dic11⋊C5)) #44568467

order32340
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C7⋊(Dic11⋊C5))
unambiguous semidirect productC3⋊(C7×C7⋊(Dic11⋊C5))
unambiguous semidirect productC7⋊(C7×C3⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊(C7×Dic21)
unambiguous semidirect productDic231⋊(C5×C7)
unambiguous semidirect product(C7×Dic231)⋊C5

Splittings

derivedC3×C7×C11 ⋊ C4×C5×C7
HallC3×C72×C11⋊C5 ⋊ C4
HallC7×Dic231 ⋊ C5
HallC72×C11⋊C5 ⋊ Dic3
HallC3×C72×C11 ⋊ C4×C5
HallC72×C11 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ C7×Dic7
HallC3×C72 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C7×Dic21
SylowC72 ⋊ C3⋊(Dic11⋊C5)
HallC3×C11 ⋊ C5×C7×Dic7
SylowC11 ⋊ C5×C7×Dic21
SylowC3 ⋊ C7×C7⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C7⋊AGL(1,𝔽11))
commutator, hypocenterC3×C7×C11C4×C5×C7
FrattiniC2C7×C3⋊(C7⋊AGL(1,𝔽11))
Fitting, socleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
cosocleC2×C3×C7×C11C2×C5×C7
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C7

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 924

Conjugacy classes & character table

1134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 169);