Finite Group Databasebeta

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C2×C3×C42×C113 #72189397

order10848
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 344064
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C113
multiplicative(ℤ/14755)ˣ, (ℤ/29510)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C113
socle, prime radicalC23×C3×C113C22
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C8×C113, C3×C43×C113, C22×C3×C42×C113, …
maximal normal subgroup ofC2×C3×C4×C8×C113, C3×C43×C113, C22×C3×C42×C113, …
maximal quotient ofC2×C3×C4×C8×C113, C3×C43×C113, C22×C3×C42×C113, …
automorphism group ofC5×C13×C227
outer automorphism group ofC5×C13×C227

GAP

Past the SmallGroups library coverage — no SmallGroups id.