Finite Group Databasebeta

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C3×C5×C7×C49 #72184496

order5145
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 98784
homologyAbelianization (H1) = G · Schur multiplier (H2) = C7

Aliases

abelianC3×C5×C7×C49

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C3×C5×C72
socle, prime radicalC3×C5×C72C7
LCSG ▷ C1
UCSC1 ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5145 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C7×C49, C5×C7×C9×C49, C32×C5×C7×C49, …
maximal normal subgroup ofC2×C3×C5×C7×C49, C5×C7×C9×C49, C32×C5×C7×C49, …
maximal quotient ofC2×C3×C5×C7×C49, C5×C7×C9×C49, C32×C5×C7×C49, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.