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C5×(C31⋊C3)⋊C4 #14272256

order1860
isoclinismisoclinic class of D31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C31⋊C3)⋊C4
unambiguous semidirect product(C5×Dic31)⋊C3

Splittings

derived, SylowC31 ⋊ C3×C4×C5
HallC5×Dic31 ⋊ C3
HallC5×C31⋊C3 ⋊ C4
HallC5×C31 ⋊ C3×C4
HallDic31 ⋊ C3×C5
HallC31⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D31⋊C3
commutator, hypocenterC31C3×C4×C5
FrattiniC2C5×D31⋊C3
Fitting, socleC2×C5×C31C2×C3
prime radicalC2×C5×C31⋊C3C2
cosocleC2×C31C2×C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 620

A minimal faithful permutation representation — 2 generators on 40 points:

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7×(C31⋊C3)⋊C4, C5×#14579596, C5×#14579595, …
maximal normal subgroup ofC5×C7×(C31⋊C3)⋊C4, C5×C11×(C31⋊C3)⋊C4, C5×C13×(C31⋊C3)⋊C4, …
maximal quotient ofC5×C7×(C31⋊C3)⋊C4, C5×#14579596, C5×#14579595, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1860, 6);