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C11×C3⋊#1043 #15693201

order3300
isoclinismisoclinic class of C3⋊#1043
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊#1043
unambiguous semidirect productC3⋊(C11×#1043)

Splittings

Fitting, socle, HallC3×C52×C11 ⋊ C4
derived, HallC3×C52 ⋊ C4×C11
HallC52×C11 ⋊ Dic3
HallC3×C11 ⋊ #1043
SylowC52 ⋊ C11×Dic3
SylowC3 ⋊ C11×#1043

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#1043
commutator, hypocenterC3×C52C4×C11
FrattiniC1G
Fitting, socleC3×C52×C11C4
prime radicalC3×C11×C5⋊D5C2
cosocleC3×C5⋊D5C2×C11
LCSG ▷ C3×C52
UCSC1 ◁ C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 825

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C11×C3⋊#1043, C11×C3⋊(C7⋊#1043), C121×C3⋊#1043, …
maximal normal subgroup ofC7×C11×C3⋊#1043, C121×C3⋊#1043, C112×C3⋊#1043
maximal quotient ofC7×C11×C3⋊#1043, C11×C3⋊(C7⋊#1043), C121×C3⋊#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 121);