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C4×C11×C52⋊C3 #15693133

order3300
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC4×C11×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C3×C11)
unambiguous semidirect product(C4×C52×C11)⋊C3

Splittings

Fitting, HallC4×C52×C11 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C11
HallC52×C11 ⋊ C3×C4
HallC4×C52 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC4×C11C52⋊C3
commutator, hypocenterC52C3×C4×C11
FrattiniC2C2×C11×C52⋊C3
FittingC4×C52×C11C3
socleC2×C52×C11C2×C3
prime radicalC2×C11×C52⋊C3C2
cosocleC2×C52C2×C3×C11
LCSG ▷ C52
UCSC1 ◁ C4×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 660

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15)(16,17,19)(18,22,24)(20,25,28)(21,27,30)(23,26,29);(16,18,23,28,30)(17,22,26,20,21)(19,25,24,27,29)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×Dic7⋊(C52⋊C3), C11×Dic7×C52⋊C3, C4×C11×C7⋊(C52⋊C3), …
maximal normal subgroup ofC4×C7×C11×C52⋊C3, C4×C52⋊C3×C121, C4×C112×C52⋊C3
maximal quotient ofC11×Dic7⋊(C52⋊C3), C11×Dic7×C52⋊C3, C4×C11×C7⋊(C52⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 53);