Finite Group Databasebeta

← Prev (#72193457) Next (#72193459) →

C3×C4×C7×C8×C23 #72193458

order15456
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 33792
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C7×C8×C23
multiplicative(ℤ/16757)ˣ, (ℤ/33514)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C3×C7×C23
socle, prime radicalC22×C3×C7×C23C2×C4
LCSG ▷ C1
UCSC1 ◁ G

176 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C7×C16×C23, C3×C7×C82×C23, C2×C3×C4×C7×C8×C23
maximal normal subgroup ofC3×C4×C7×C16×C23, C3×C7×C82×C23, C2×C3×C4×C7×C8×C23
maximal quotient ofC3×C4×C7×C16×C23, C3×C7×C82×C23, C2×C3×C4×C7×C8×C23
automorphism group ofC13×C1289
outer automorphism group ofC13×C1289

GAP

Past the SmallGroups library coverage — no SmallGroups id.