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C3×C11×#1039 #15693137

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

Aliases

direct productC3×C11×#1039

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C5⋊D5
commutator, hypocenterC52C3×C4×C11
FrattiniC2C3×C11×C5⋊D5
Fitting, socle, prime radicalC2×C3×C52×C11C2
cosocleC2×C52C2×C3×C11
LCSG ▷ C52
UCSC1 ◁ C2×C3×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)(4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18)(20,21)(22,23)(25,26)(27,28);(24,25,27,28,26);(19,20,22,23,21)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×ΓL(1,𝔽8)⋊#1039, C11×ΓL(1,𝔽8)×#1039, C3×C11×C7⋊#1039, …
maximal normal subgroup ofC3×C7×C11×#1039, C3×#1039×C121, C3×C112×#1039
maximal quotient ofC11×ΓL(1,𝔽8)⋊#1039, C11×ΓL(1,𝔽8)×#1039, C3×C11×C7⋊#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 57);