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C22×C33×C4×C52 #72189355

order10800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1035141120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C33×C5

Aliases

abelianC22×C33×C4×C52
multiplicative(ℤ/13237)ˣ, (ℤ/17019)ˣ, (ℤ/26474)ˣ, (ℤ/34038)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C33×C52
socle, prime radicalC23×C33×C52C2
LCSG ▷ C1
UCSC1 ◁ G

6048 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×C33×C52×C8, C2×C33×C42×C52, C23×C33×C4×C52, …
maximal normal subgroup ofC22×C33×C52×C8, C2×C33×C42×C52, C23×C33×C4×C52, …
maximal quotient ofC22×C33×C52×C8, C2×C33×C42×C52, C23×C33×C4×C52, …
automorphism group ofC7×C31×C61
outer automorphism group ofC7×C31×C61

GAP

Past the SmallGroups library coverage — no SmallGroups id.