Finite Group Databasebeta

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C2×C3×C42×C7×C17 #72189889

order11424
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 294912
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C7×C17
multiplicative(ℤ/14935)ˣ, (ℤ/15535)ˣ, (ℤ/21435)ˣ, (ℤ/22864)ˣ, (ℤ/28580)ˣ, (ℤ/29870)ˣ, (ℤ/31070)ˣ, (ℤ/42870)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C7×C17
socle, prime radicalC23×C3×C7×C17C22
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C7×C8×C17, C3×C43×C7×C17, C22×C3×C42×C7×C17
maximal normal subgroup ofC2×C3×C4×C7×C8×C17, C3×C43×C7×C17, C22×C3×C42×C7×C17
maximal quotient ofC2×C3×C4×C7×C8×C17, C3×C43×C7×C17, C22×C3×C42×C7×C17
automorphism group ofC5×C29×C103, C5×C13×C239
outer automorphism group ofC5×C29×C103, C5×C13×C239

GAP

Past the SmallGroups library coverage — no SmallGroups id.