Finite Group Databasebeta

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C22×C42×C7×C27 #72190489

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15925248
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C42×C7×C27
multiplicative(ℤ/25288)ˣ, (ℤ/30280)ˣ, (ℤ/30320)ˣ, (ℤ/36336)ˣ, (ℤ/37584)ˣ, (ℤ/37932)ˣ, (ℤ/45420)ˣ, (ℤ/46980)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C9C24×C3×C7
socle, prime radicalC24×C3×C7C22×C9
LCSG ▷ C1
UCSC1 ◁ G

1992 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C7×C8×C27, C2×C43×C7×C27, C23×C42×C7×C27
maximal normal subgroup ofC22×C4×C7×C8×C27, C2×C43×C7×C27, C23×C42×C7×C27
maximal quotient ofC22×C4×C7×C8×C27, C2×C43×C7×C27, C23×C42×C7×C27
automorphism group ofC8×C29×C109, C5×C8×C757, C5×C16×C379
outer automorphism group ofC8×C29×C109, C5×C8×C757, C5×C16×C379

GAP

Past the SmallGroups library coverage — no SmallGroups id.