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C2×C5×C8×C27 #72182145

order2160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1152
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C8×C27
multiplicative(ℤ/3321)ˣ, (ℤ/6642)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C9C22×C3×C5
socle, prime radicalC22×C3×C5C4×C9
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C16×C27, C4×C5×C8×C27, C22×C5×C8×C27, …
maximal normal subgroup ofC2×C5×C16×C27, C4×C5×C8×C27, C22×C5×C8×C27, …
maximal quotient ofC2×C5×C16×C27, C4×C5×C8×C27, C22×C5×C8×C27, …
automorphism group ofC41×C81, C2×C41×C81
outer automorphism group ofC41×C81, C2×C41×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.