Finite Group Databasebeta

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C3×C7⋊(C7⋊(Dic11⋊C5)) #44568463

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×C7⋊(C7⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊(C3×C7⋊Dic7)
unambiguous semidirect product(C3×C7⋊Dic77)⋊C5

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC3×C72×C11⋊C5 ⋊ C4
HallC3×C7⋊Dic77 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC7⋊Dic77 ⋊ C3×C5
HallC3×C72×C11 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ C7⋊Dic7
HallC3×C72 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ C3×Dic11⋊C5
HallC3×C11 ⋊ C5×C7⋊Dic7
SylowC11 ⋊ C3×C5×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C3C7⋊(C7⋊AGL(1,𝔽11))
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C3×C7⋊(C7⋊AGL(1,𝔽11))
Fitting, socleC2×C3×C72×C11C2×C5
prime radicalC2×C3×C72×C11⋊C5C2
cosocleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 124 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) = 6468

Conjugacy classes & character table

1074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 165);