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C3×C7×D5×C11 #14556324

order2310
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D5×C11
unambiguous semidirect productC5⋊(C2×C3×C7×C11)

Splittings

Fitting, socle, HallC3×C5×C7×C11 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C7×C11
HallC5×C7×C11 ⋊ C2×C3
HallC3×C5×C11 ⋊ C2×C7
HallC3×C5×C7 ⋊ C2×C11
HallC5×C11 ⋊ C2×C3×C7
HallC5×C7 ⋊ C2×C3×C11
HallC3×C5 ⋊ C2×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D5
commutator, cosocle, hypocenterC5C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C11C2
LCSG ▷ C5
UCSC1 ◁ C3×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1155

A minimal faithful permutation representation — 2 generators on 26 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C7×C11×AGL(1,𝔽5), C3×C7×C11⋊AGL(1,𝔽5), C3×C11×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×C7×C11×AGL(1,𝔽5), C3×C7×C11⋊AGL(1,𝔽5), C3×C11×C7⋊AGL(1,𝔽5), …
maximal quotient ofC3×C7×C11×Dic5, C2×C3×C7×D5×C11, C3×C7×C11×D25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2310, 8);