Finite Group Databasebeta

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C5×D3×C11×C7⋊D7 #44568853

order32340
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC5×D3×C11×C7⋊D7
unambiguous semidirect product(D3×C7)⋊(C5×C11×D7)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C22
derived, HallC3×C72 ⋊ C22×C5×C11
HallC5×C72×C11 ⋊ C2×D3
HallC3×C72×C11 ⋊ C22×C5
HallC3×C5×C72 ⋊ C22×C11
HallC72×C11 ⋊ C2×C5×D3
HallC5×C72 ⋊ C2×D3×C11
HallC3×C5×C11 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C5×D3×C11
HallC3×C11 ⋊ C2×C5×C7⋊D7
HallC3×C5 ⋊ C2×C11×C7⋊D7
SylowC3 ⋊ C2×C5×C11×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC5×C11D3×C7⋊D7
commutator, cosocle, hypocenterC3×C72C22×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C22
LCSG ▷ C3×C72
UCSC1 ◁ C5×C11

400 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 8085

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 555);