Finite Group Databasebeta

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C2×C3×C11⋊C5×C7⋊D7 #44568753

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C11⋊C5×C7⋊D7
unambiguous semidirect product(C2×C3×C11×C7⋊D7)⋊C5

Splittings

Fitting, socleC2×C3×C72×C11 ⋊ C2×C5
derived, HallC72×C11 ⋊ C22×C3×C5
HallC3×C72×C11⋊C5 ⋊ C22
HallC2×C3×C11×C7⋊D7 ⋊ C5
HallC72×C11⋊C5 ⋊ C22×C3
HallC2×C11×C7⋊D7 ⋊ C3×C5
HallC3×C72×C11 ⋊ C22×C5
HallC3×C72 ⋊ C22×C11⋊C5
SylowC72 ⋊ C22×C3×C11⋊C5
HallC3×C11 ⋊ C2×C5×C7⋊D7
SylowC11 ⋊ C2×C3×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×C7⋊D7
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C72×C11C2×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C3

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3234

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 455);