Finite Group Databasebeta

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C2×C3×C27×C49 #72186838

order7938
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 13608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC2×C3×C27×C49

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7×C9C2×C32×C7
socle, prime radicalC2×C32×C7C7×C9
LCSG ▷ C1
UCSC1 ◁ G

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7938 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C27×C49, C22×C3×C27×C49, C2×C3×C49×C81, …
maximal normal subgroup ofC3×C4×C27×C49, C22×C3×C27×C49, C2×C3×C49×C81, …
maximal quotient ofC3×C4×C27×C49, C22×C3×C27×C49, C2×C3×C49×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.