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C3×C5×#3866 #14555697

order2220
isoclinismisoclinic class of #3866
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×#3866

Splittings

Fitting, socle, HallC3×C5×C37 ⋊ C4
derived, SylowC37 ⋊ C3×C4×C5
HallC5×C37 ⋊ C3×C4
HallC3×C37 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5#3866
commutator, hypocenterC37C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C37C4
prime radicalC3×C5×D37C2
cosocleD37C2×C3×C5
LCSG ▷ C37
UCSC1 ◁ C3×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 555

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2,3)(4,5,6,7,8)(10,11,12,14)(13,16,17,23)(15,20,21,19)(18,25,26,34)(22,29,27,30)(24,31,32,28)(33,38,39,37)(35,40,41,36)(42,44,45,43);(9,10,13,18,27,21,14,19,28,36,39,32,23,30,37,43,45,41,34,25,35,42,44,38,29,16,24,33,40,31,20,11,15,22,26,17,12)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C25×#3866, C3×C52×#3866, C3×C5×#10625191, …
maximal normal subgroup ofC3×C25×#3866, C3×C52×#3866, C3×C5×C7×#3866, …
maximal quotient ofC3×C25×#3866, C3×C52×#3866, C3×C5×#10625191, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2220, 24);