Finite Group Databasebeta

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C2×C4×C7×C113 #72185481

order6328
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5376
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C7×C113
multiplicative(ℤ/6583)ˣ, (ℤ/7915)ˣ, (ℤ/13166)ˣ, (ℤ/15830)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C7×C113
socle, prime radicalC22×C7×C113C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6328 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C8×C113, C42×C7×C113, C22×C4×C7×C113, …
maximal normal subgroup ofC2×C7×C8×C113, C42×C7×C113, C22×C4×C7×C113, …
maximal quotient ofC2×C7×C8×C113, C42×C7×C113, C22×C4×C7×C113, …
automorphism group ofC29×C227, C5×C1583
outer automorphism group ofC29×C227, C5×C1583

GAP

Past the SmallGroups library coverage — no SmallGroups id.