Finite Group Databasebeta

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C24×#525 #72268525

order1024
nilpotency class2
automorphism?
homologyAbelianization (H1) = C28 · Schur multiplier (H2) = C227

Aliases

direct productC24×#525

Subgroups

subgroupG/H
center, socleC25×C4C23
commutator, Frattini, cosocleC22C28
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C25×C4 ◁ G
LECSG ▷ C22 ▷ C1

1060245 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 256

Conjugacy classes & character table

448 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×D4×#525, C2×#72267396, C22×#393988, …
maximal normal subgroup ofC22×D4×#525, C2×#72267396, C22×#393988, …
maximal quotient ofC22×D4×#525, C23×#36096, C23×#34655, …
automorphism group of#13107, #13128

GAP

Past the SmallGroups library coverage — no SmallGroups id.