Finite Group Databasebeta

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C2×C5×C11×#64424 #44568770

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×#64424

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2×C3
derived, SylowC72 ⋊ C22×C3×C5×C11
HallC2×C5×C11×C7⋊D7 ⋊ C3
HallC5×C11×#3861 ⋊ C22
HallC5×C72×C11 ⋊ C22×C3
HallC2×C11×C7⋊D7 ⋊ C3×C5
HallC11×#3861 ⋊ C22×C5
HallC2×C5×C7⋊D7 ⋊ C3×C11
HallC5×#3861 ⋊ C22×C11
HallC72×C11 ⋊ C22×C3×C5
HallC5×C72 ⋊ C22×C3×C11
HallC2×C7⋊D7 ⋊ C3×C5×C11
Hall#3861 ⋊ C22×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11#64424
commutator, cosocle, hypocenterC72C22×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2×C3
LCSG ▷ C72
UCSC1 ◁ C2×C5×C11

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5390

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 472);