Finite Group Databasebeta

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C22×C4×C7×C113 #72191000

order12656
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 129024
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C7×C113
multiplicative(ℤ/19749)ˣ, (ℤ/23745)ˣ, (ℤ/25328)ˣ, (ℤ/26332)ˣ, (ℤ/31660)ˣ, (ℤ/39498)ˣ, (ℤ/47490)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C7×C113
socle, prime radicalC23×C7×C113C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12656 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C7×C8×C113, C2×C42×C7×C113, C23×C4×C7×C113
maximal normal subgroup ofC22×C7×C8×C113, C2×C42×C7×C113, C23×C4×C7×C113
maximal quotient ofC22×C7×C8×C113, C2×C42×C7×C113, C23×C4×C7×C113

GAP

Past the SmallGroups library coverage — no SmallGroups id.