Finite Group Databasebeta

← Prev (#6358357) Next (#6358359) →

Cayley diagram

C2×D8×SD16 #6358358

order512
nilpotency class3
isoclinismisoclinic class of D82
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×D8×SD16

Subgroups

subgroupG/H
center, socleC23D42
commutator, Frattini, cosocleC42C25
prime radicalC2×D4×D8C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

2374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 128

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofSD16×#442, #72279433, C2×D8×AGL(1,ℤ/8), …
maximal normal subgroup ofSD16×#442, #72279433, C2×D8×AGL(1,ℤ/8), …
maximal quotient of#72309684, #72309977, C2×#244792, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6265554);