Finite Group Databasebeta

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C2×C3×C4×C7×C97 #72194236

order16296
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9216
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C7×C97
multiplicative(ℤ/16727)ˣ, (ℤ/19061)ˣ, (ℤ/33454)ˣ, (ℤ/38122)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C7×C97
socle, prime radicalC22×C3×C7×C97C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16296 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C7×C8×C97, C3×C42×C7×C97, C22×C3×C4×C7×C97
maximal normal subgroup ofC2×C3×C7×C8×C97, C3×C42×C7×C97, C22×C3×C4×C7×C97
maximal quotient ofC2×C3×C7×C8×C97, C3×C42×C7×C97, C22×C3×C4×C7×C97
automorphism group ofC43×C389
outer automorphism group ofC43×C389

GAP

Past the SmallGroups library coverage — no SmallGroups id.