Finite Group Databasebeta

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C2×#72225051 #72285401

order2048
nilpotency class4
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC2×#72225051

Subgroups

subgroupG/H
center, socleC24C2×#442
commutatorC2×C8C24×C8
Frattini, cosocleC2×C4×C8C25
prime radicalC22×#2184C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ C23×#322 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

14680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 512

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72286863, C2×D4×#12067, C2×#72225133, …
maximal normal subgroup of#72286863, C2×D4×#12067, C2×#72225133, …
maximal quotient ofC2×#72225052, #72286863, C2×#72225088, …
automorphism group of#7418, #7419, #7420, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.