Finite Group Databasebeta

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C2×#6628883 #72249692

order1024
nilpotency class3
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C217

Aliases

direct productC2×#6628883

Subgroups

subgroupG/H
center, socleC22C2×#2846
commutator, Frattini, cosocleC22×C4C26
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

228163 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 64

Conjugacy classes & character table

178 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC2×#72233783, C2×#72241002, C2×#72241001
maximal subgroup of#72249800, C2×#72236873, C2×#72231746, …
maximal normal subgroup of#72249800, C2×#72236873, C2×#72231746, …
maximal quotient of#72249924, #72282766, #72282806, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.