Finite Group Databasebeta

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C22×C3×C7×C8×C17 #72189888

order11424
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 73728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C7×C8×C17
multiplicative(ℤ/17673)ˣ, (ℤ/20013)ˣ, (ℤ/20139)ˣ, (ℤ/22856)ˣ, (ℤ/23564)ˣ, (ℤ/26684)ˣ, (ℤ/26852)ˣ, (ℤ/34284)ˣ, (ℤ/34308)ˣ, (ℤ/35346)ˣ, (ℤ/40026)ˣ, (ℤ/40278)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C3×C7×C17
socle, prime radicalC23×C3×C7×C17C4
LCSG ▷ C1
UCSC1 ◁ G

304 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 ofC22×C3×C7×C16×C17, C2×C3×C4×C7×C8×C17, C23×C3×C7×C8×C17
maximal normal subgroup ofC22×C3×C7×C16×C17, C2×C3×C4×C7×C8×C17, C23×C3×C7×C8×C17
maximal quotient ofC22×C3×C7×C16×C17, C2×C3×C4×C7×C8×C17, C23×C3×C7×C8×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.