Finite Group Databasebeta

C2×#6573730 #72249455

order1024
nilpotency class3
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productC2×#6573730

Subgroups

subgroupG/H
center, socleC22D4×#120
commutator, Frattini, cosocleC22×C4C26
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

42429 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 64

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC2×#72236874, C2×#72240995, C2×#72240996
maximal subgroup ofC2×#72236873, C2×#72237521, C2×#72237525, …
maximal normal subgroup ofC2×#72236873, C2×#72237521, C2×#72237525, …
maximal quotient of#72306523, #72315924, #72316200, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.