Finite Group Databasebeta

← Prev (#7700122) Next (#7700124) →

Cayley diagram

C2×#46642 #7700123

order512
nilpotency class2
isoclinismisoclinic class of #46350
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C212

Aliases

direct productC2×#46642

Subgroups

subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

6942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 128

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(11,12)(13,17)(14,16)(15,18)(19,20,23,25)(21,22,26,24);(3,4)(5,9)(6,7)(8,10)(11,12,14,16)(13,15,18,17)(19,21,23,26)(20,24,25,22);(4,7)(8,9)(19,22)(20,21)(23,24)(25,26);(3,4)(5,8)(6,7)(9,10)(11,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,26)(24,25);(3,5)(4,8)(6,10)(7,9)(11,13,14,18)(12,15,16,17)(19,22)(20,21)(23,24)(25,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#8077160, C2×#8509094, C2×#8903076
maximal normal subgroup ofC2×#8077160, C2×#8509094, C2×#8903076
maximal quotient ofC2×#4037089

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7607319);