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C5×#20258973 #44478193

order30420
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×#20258973

Splittings

Fitting, socle, HallC32×C5×C132 ⋊ C4
derived, HallC32×C132 ⋊ C4×C5
HallC5×C132 ⋊ #157
SylowC132 ⋊ C5×#157
HallC32×C5 ⋊ #10621728
SylowC32 ⋊ C5×#10621728

Subgroups

subgroupG/H
center, hypercenterC5#20258973
commutator, hypocenterC32×C132C4×C5
FrattiniC1G
Fitting, socleC32×C5×C132C4
prime radicalC5×C3⋊(C3⋊(C13⋊D13))C2
cosocleC3⋊(C3⋊(C13⋊D13))C2×C5
LCSG ▷ C32×C132
UCSC1 ◁ C5

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 5070

A minimal faithful permutation representation — 3 generators on 37 points:

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

Conjugacy classes & character table

1920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 782);