Finite Group Databasebeta

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C2×C3×C4×C5×C97 #72190065

order11640
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6144
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C5×C97
multiplicative(ℤ/12059)ˣ, (ℤ/12623)ˣ, (ℤ/17463)ˣ, (ℤ/23284)ˣ, (ℤ/24118)ˣ, (ℤ/25246)ˣ, (ℤ/34926)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C5×C97
socle, prime radicalC22×C3×C5×C97C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C8×C97, C3×C42×C5×C97, C22×C3×C4×C5×C97
maximal normal subgroup ofC2×C3×C5×C8×C97, C3×C42×C5×C97, C22×C3×C4×C5×C97
maximal quotient ofC2×C3×C5×C8×C97, C3×C42×C5×C97, C22×C3×C4×C5×C97
automorphism group ofC31×C389, C13×C971
outer automorphism group ofC31×C389, C13×C971

GAP

Past the SmallGroups library coverage — no SmallGroups id.