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C22×C4×C52×C27 #72189351

order10800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1658880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C5

Aliases

abelianC22×C4×C52×C27
multiplicative(ℤ/14905)ˣ, (ℤ/17853)ˣ, (ℤ/20325)ˣ, (ℤ/22275)ˣ, (ℤ/23804)ˣ, (ℤ/27100)ˣ, (ℤ/29810)ˣ, (ℤ/35706)ˣ, (ℤ/40650)ˣ, (ℤ/44550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C23×C3×C52
socle, prime radicalC23×C3×C52C2×C9
LCSG ▷ C1
UCSC1 ◁ G

864 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C52×C8×C27, C2×C42×C52×C27, C23×C4×C52×C27, …
maximal normal subgroup ofC22×C52×C8×C27, C2×C42×C52×C27, C23×C4×C52×C27, …
maximal quotient ofC22×C52×C8×C27, C2×C42×C52×C27, C23×C4×C52×C27, …
automorphism group ofC11×C25×C81
outer automorphism group ofC11×C25×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.