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C5×#4428 #11745702

order945
isoclinismisoclinic class of #4427
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#4428

Splittings

FittingC5×C7×C9 ⋊ C3
HallC5×C7 ⋊ 3−1+2
SylowC7 ⋊ C5×3−1+2

Subgroups

subgroupG/H
centerC3×C5C3×ΓL(1,𝔽8)
commutator, cosocleC3×C7C32×C5
FrattiniC3C3×C5×ΓL(1,𝔽8)
FittingC5×C7×C9C3
socleC3×C5×C7C32
prime radicalC3×C5×ΓL(1,𝔽8)C3
hypercenterC5×C9ΓL(1,𝔽8)
hypocenterC7C5×3−1+2
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C3×C5 ◁ C5×C9

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 315

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#67355, D5×#4428, C5⋊#67355, …
maximal normal subgroup ofC5×#67355, D5×#4428, C5⋊#67355, …
maximal quotient ofC2×C5×#4428

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(945, 5);