Finite Group Databasebeta

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C23×C3×C4×C5×C7×C8 #72203973

order26880
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4227858432
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C3×C4×C5×C7×C8
multiplicative(ℤ/66584)ˣ, (ℤ/70520)ˣ, (ℤ/71456)ˣ, (ℤ/75680)ˣ, (ℤ/78680)ˣ, (ℤ/79520)ˣ, (ℤ/80360)ˣ, (ℤ/84624)ˣ, (ℤ/85608)ˣ, (ℤ/86240)ˣ, (ℤ/86304)ˣ, (ℤ/87672)ˣ, (ℤ/88608)ˣ, (ℤ/91872)ˣ, (ℤ/94416)ˣ, (ℤ/96432)ˣ, (ℤ/99876)ˣ, (ℤ/101160)ˣ, (ℤ/101280)ˣ, (ℤ/102240)ˣ, (ℤ/103200)ˣ, (ℤ/105780)ˣ, (ℤ/117600)ˣ, (ℤ/118020)ˣ, (ℤ/120540)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C25×C3×C5×C7
socle, prime radicalC25×C3×C5×C7C2×C4
LCSG ▷ C1
UCSC1 ◁ G

18552 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

26880 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.