Finite Group Databasebeta

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C22×C3×C5×C8×C29 #72192133

order13920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 86016
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C5×C8×C29
multiplicative(ℤ/16933)ˣ, (ℤ/17941)ˣ, (ℤ/21669)ˣ, (ℤ/21771)ˣ, (ℤ/23067)ˣ, (ℤ/28892)ˣ, (ℤ/33866)ˣ, (ℤ/35882)ˣ, (ℤ/43338)ˣ, (ℤ/43542)ˣ, (ℤ/46134)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C3×C5×C29
socle, prime radicalC23×C3×C5×C29C4
LCSG ▷ C1
UCSC1 ◁ G

304 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C16×C29, C2×C3×C4×C5×C8×C29, C23×C3×C5×C8×C29
maximal normal subgroup ofC22×C3×C5×C16×C29, C2×C3×C4×C5×C8×C29, C23×C3×C5×C8×C29
maximal quotient ofC22×C3×C5×C16×C29, C2×C3×C4×C5×C8×C29, C23×C3×C5×C8×C29
automorphism group ofC7×C41×C59, C7×C11×C233
outer automorphism group ofC7×C41×C59, C7×C11×C233

GAP

Past the SmallGroups library coverage — no SmallGroups id.