Finite Group Databasebeta

← Prev (#65721) Next (#65723) →

Cayley diagram

C2×#3995 #65722

order320
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#3995

Splittings

SylowC5 ⋊ C2×#108

Subgroups

subgroupG/H
centerC22C4⋊AGL(1,𝔽5)
commutatorC4×C5C22×C4
FrattiniC4C22×AGL(1,𝔽5)
FittingC2×C5×C8C4
socleC22×C5C4⋊C4
prime radicalC22×D5Q8
cosocleC4×D5C23
hypercenterC2×C8AGL(1,𝔽5)
hypocenterC5C2×#108
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 23 points:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10598622, #10598628, #10598663, …
maximal normal subgroup of#10598622, #10598628, #10598663, …
maximal quotient of#10603814, #10603816, #10603819, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1060);