Finite Group Databasebeta

← Prev (#62717) Next (#62719) →

Cayley diagram

C2×#3532 #62718

order256
nilpotency class2
isoclinismisoclinic class of #3532
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#3532

Subgroups

subgroupG/H
center, socleC23C25
commutator, Frattini, cosocleC22C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

4771 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 32

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC2×#3532⋊C3, #72261513
maximal subgroup ofC2×#12753, #493582, #511779, …
maximal normal subgroup ofC2×#12753, #493582, #511779, …
maximal quotient ofC2×#34356, C2×#34407, C2×#34416, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55706);