Finite Group Databasebeta

← Prev (#10577550) Next (#10577552) →

Cayley diagram

C2×#62296 #10577551

order512
nilpotency class3
isoclinismisoclinic class of #62295
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#62296

Subgroups

subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
prime radicalC2×#3519C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

6918 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);(3,4)(5,9)(6,8)(7,10)(11,12)(13,20)(14,18)(15,24)(16,19)(17,21)(22,25)(23,26);(3,5)(4,7)(6,10)(8,9);(11,13,15,21,16,22,14,23)(12,17,18,20,19,26,24,25);(5,10)(7,9);(4,8)(7,9)(11,14,16,15)(12,18,19,24)(13,21,22,23)(17,25,26,20)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#10583262, C2×#10583218, C2×#10577656
maximal normal subgroup ofC2×#10583262, C2×#10583218, C2×#10577656

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484747);