Finite Group Databasebeta

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C3×C4×C5×C11×C11⋊C5 #49137302

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C4×C5×C11×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C3×C52×C11)
unambiguous semidirect product(C3×C4×C11)⋊(C52×C11)
unambiguous semidirect product(C4×C5×C11)⋊(C3×C5×C11)
unambiguous semidirect product(C3×C4×C5×C11)⋊(C5×C11)

Splittings

FittingC3×C4×C5×C112 ⋊ C5
derivedC11 ⋊ C3×C4×C52×C11
HallC3×C4×C112 ⋊ C52
HallC4×C112 ⋊ C3×C52
HallC3×C112 ⋊ C4×C52
SylowC112 ⋊ C3×C4×C52

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C11C11⋊C5
commutator, hypocenterC11C3×C4×C52×C11
FrattiniC2C2×C3×C5×C11×C11⋊C5
FittingC3×C4×C5×C112C5
socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C11C2×C3×C52×C11
LCSG ▷ C11
UCSC1 ◁ C3×C4×C5×C11

216 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 3300

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 438);