Finite Group Databasebeta

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C2×#72209716 #72217296

order2048
nilpotency class3
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C215

Aliases

direct productC2×#72209716

Subgroups

subgroupG/H
center, socleC23#15947
commutator, Frattini, cosocleC26C25
LCSG ▷ C26 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C27 ◁ G
LECSG ▷ C26 ▷ C22 ▷ C1

2144864 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC2×#72210409, C2×#72210665, C2×#72216208, …
maximal subgroup of#72252587, C2×#72210409, C2×#72215688, …
maximal normal subgroup ofC2×#72210568, #72252587, C2×#72210409, …
automorphism group ofC4×C22⋊C4, C3×#563

GAP

Past the SmallGroups library coverage — no SmallGroups id.