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C2×C5×#1795 #11943341

order1280
nilpotency class3
isoclinismisoclinic class of #1795
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C28

Aliases

direct productC2×C5×#1795

Subgroups

subgroupG/H
center, socleC22×C5#379
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×H(5,𝔽2)C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

3946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 4 generators on 23 points:

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

Conjugacy classes & character table

290 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×#23872
maximal normal subgroup ofC2×C5×#23872

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 13609);