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C2×C3×C4×C52×C27 #72194172

order16200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1244160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3×C5

Aliases

abelianC2×C3×C4×C52×C27
multiplicative(ℤ/16531)ˣ, (ℤ/16771)ˣ, (ℤ/33062)ˣ, (ℤ/33542)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C22×C32×C52
socle, prime radicalC22×C32×C52C2×C9
LCSG ▷ C1
UCSC1 ◁ G

896 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C52×C8×C27, C3×C42×C52×C27, C22×C3×C4×C52×C27
maximal normal subgroup ofC2×C3×C52×C8×C27, C3×C42×C52×C27, C22×C3×C4×C52×C27
maximal quotient ofC2×C3×C52×C8×C27, C3×C42×C52×C27, C22×C3×C4×C52×C27
automorphism group ofC61×C271, C31×C541
outer automorphism group ofC61×C271, C31×C541

GAP

Past the SmallGroups library coverage — no SmallGroups id.