Finite Group Databasebeta

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C26×C3×C4×C16 #72190683

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order ≥ 263
homologyAbelianization (H1) = G · Schur multiplier (H2) = C227×C4

Aliases

abelianC26×C3×C4×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C28×C3
socle, prime radicalC28×C3C2×C8
LCSG ▷ C1
UCSC1 ◁ G

8277494 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC26×C3×C4×C32, C26×C3×C8×C16, C25×C3×C42×C16, …
maximal normal subgroup ofC26×C3×C4×C32, C26×C3×C8×C16, C25×C3×C42×C16, …
maximal quotient ofC26×C3×C4×C32, C26×C3×C8×C16, C25×C3×C42×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.