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C11×C3⋊#1039 #15693143

order3300
isoclinismisoclinic class of C3⋊(C5⋊D5)
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×C3⋊#1039
unambiguous semidirect productC3⋊(C11×#1039)

Splittings

derived, HallC3×C52 ⋊ C4×C11
HallC3×C52×C11 ⋊ C4
HallC52×C11 ⋊ Dic3
HallC3×C11 ⋊ #1039
SylowC52 ⋊ C11×Dic3
SylowC3 ⋊ C11×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C4×C11
FrattiniC2C11×C3⋊(C5⋊D5)
Fitting, socle, prime radicalC2×C3×C52×C11C2
cosocleC2×C3×C52C2×C11
LCSG ▷ C3×C52
UCSC1 ◁ C2×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 3300

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×C3⋊(C7⋊#1039), C7×C11×C3⋊#1039, C121×C3⋊#1039, …
maximal normal subgroup ofC7×C11×C3⋊#1039, C121×C3⋊#1039, C112×C3⋊#1039
maximal quotient ofC11×C3⋊(C7⋊#1039), C7×C11×C3⋊#1039, C121×C3⋊#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 63);