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C3×C11×#1044 #15693185

order3300
isoclinismisoclinic class of #1044
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C11×#1044

Splittings

Fitting, socle, HallC3×C52×C11 ⋊ C4
derived, SylowC52 ⋊ C3×C4×C11
HallC52×C11 ⋊ C3×C4
HallC3×C52 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11#1044
commutator, hypocenterC52C3×C4×C11
FrattiniC1G
Fitting, socleC3×C52×C11C4
prime radicalC3×C11×C5⋊D5C2
cosocleC5⋊D5C2×C3×C11
LCSG ▷ C52
UCSC1 ◁ C3×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 330

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×ΓL(1,𝔽8)⋊#1044, C11×ΓL(1,𝔽8)×#1044, C3×C7×C11×#1044, …
maximal normal subgroup ofC3×C7×C11×#1044, C3×#1044×C121, C3×C112×#1044
maximal quotient ofC11×ΓL(1,𝔽8)⋊#1044, C11×ΓL(1,𝔽8)×#1044, C3×C7×C11×#1044, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 105);