Finite Group Databasebeta

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C3×C7×C7⋊(C11⋊AGL(1,𝔽5)) #44568814

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C7⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C3×C7×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derivedC5×C7×C11 ⋊ C3×C4×C7
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
HallC5×C72 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ C7×Dic7
HallC3×C72 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ C3×C7×Dic7
SylowC72 ⋊ C3×C11⋊AGL(1,𝔽5)
HallC3×C11 ⋊ C7×C7⋊AGL(1,𝔽5)
HallC3×C5 ⋊ C7×Dic77
SylowC11 ⋊ C3×C7×C7⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×C7×Dic77

Subgroups

subgroupG/H
center, hypercenterC3×C7C7⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C11C3×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C72×D5×C11C2
cosocleC7×D5×C11C2×C3×C7
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3×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) = 2310

Conjugacy classes & character table

3297 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 516);