Finite Group Databasebeta

← Prev (#10574136) Next (#10574138) →

Cayley diagram

C23×C4×SD16 #10574137

order512
nilpotency class3
isoclinismisoclinic class of D8
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC23×C4×SD16

Subgroups

subgroupG/H
centerC24×C4D4
commutatorC4C25×C4
Frattini, cosocleC2×C4C26
socleC25C2×D4
prime radicalC24×D4C22
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C4 ◁ C23×C42 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

12834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 256

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×C4×AGL(1,ℤ/8), C23×#3274, C23×D4×SD16, …
maximal normal subgroup ofC23×C4×AGL(1,ℤ/8), C23×#3274, C23×D4×SD16, …
maximal quotient ofC23×#1864, C22×#22874, C22×#23022, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481333);