Finite Group Databasebeta

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C24×C32×C5×C11 #72186835

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 38707200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC24×C32×C5×C11
multiplicative(ℤ/14973)ˣ, (ℤ/15477)ˣ, (ℤ/15939)ˣ, (ℤ/16616)ˣ, (ℤ/18536)ˣ, (ℤ/19964)ˣ, (ℤ/20636)ˣ, (ℤ/23832)ˣ, (ℤ/24924)ˣ, (ℤ/25668)ˣ, (ℤ/26532)ˣ, (ℤ/27804)ˣ, (ℤ/29946)ˣ, (ℤ/30492)ˣ, (ℤ/30954)ˣ, (ℤ/31878)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

1608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C32×C4×C5×C11, C25×C32×C5×C11, C24×C3×C5×C9×C11, …
maximal normal subgroup ofC23×C32×C4×C5×C11, C25×C32×C5×C11, C24×C3×C5×C9×C11, …
maximal quotient ofC23×C32×C4×C5×C11, C25×C32×C5×C11, C24×C3×C5×C9×C11, …
automorphism group ofC8×C31×C67, C7×C8×C331, C8×C9×C331
outer automorphism group ofC8×C31×C67, C7×C8×C331, C8×C9×C331

GAP

Past the SmallGroups library coverage — no SmallGroups id.