Finite Group Databasebeta

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#1202 #72215646

order1024
nilpotency class2
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C217

Aliases

direct product#1202

Subgroups

subgroupG/H
center, commutator, Frattini, socle, cosocleC24C26
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

196792 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72215688, #120×#1020, #72225615, …
maximal normal subgroup of#72215688, #72216662, #72225615, …
maximal quotient of#72241306, #72264999, #72266787, …
automorphism group of#547, #554, #556, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.