Finite Group Databasebeta

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C5×C11×#10596872 #44568480

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#10596872

Splittings

derived, SylowC72 ⋊ C3×C4×C5×C11
HallC5×C7×C11×Dic7 ⋊ C3
HallC5×C11×#3862 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC7×C11×Dic7 ⋊ C3×C5
HallC11×#3862 ⋊ C4×C5
HallC5×C7×Dic7 ⋊ C3×C11
HallC5×#3862 ⋊ C4×C11
HallC72×C11 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×C4×C11
HallC7×Dic7 ⋊ C3×C5×C11
Hall#3862 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11#64422
commutator, hypocenterC72C3×C4×C5×C11
FrattiniC2C5×C11×#64422
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3862C2
cosocleC2×C72C2×C3×C5×C11
LCSG ▷ C72
UCSC1 ◁ C2×C5×C11

104 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 104 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) = 4620

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 182);