Finite Group Databasebeta

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C23×C3×C4×C5×C49 #72200865

order23520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7225344
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C4×C5×C49
multiplicative(ℤ/45507)ˣ, (ℤ/48856)ˣ, (ℤ/51064)ˣ, (ℤ/51555)ˣ, (ℤ/54992)ˣ, (ℤ/56595)ˣ, (ℤ/58840)ˣ, (ℤ/60368)ˣ, (ℤ/60676)ˣ, (ℤ/68600)ˣ, (ℤ/68740)ˣ, (ℤ/70608)ˣ, (ℤ/70704)ˣ, (ℤ/73284)ˣ, (ℤ/75460)ˣ, (ℤ/76596)ˣ, (ℤ/78012)ˣ, (ℤ/88260)ˣ, (ℤ/88380)ˣ, (ℤ/91014)ˣ, (ℤ/102900)ˣ, (ℤ/103110)ˣ, (ℤ/113190)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C7C24×C3×C5×C7
socle, prime radicalC24×C3×C5×C7C2×C7
LCSG ▷ C1
UCSC1 ◁ G

1416 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

23520 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.