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C2×C3×C4×C271 #72185644

order6504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C271
multiplicative(ℤ/8135)ˣ, (ℤ/9759)ˣ, (ℤ/13012)ˣ, (ℤ/16270)ˣ, (ℤ/19518)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C271
socle, prime radicalC22×C3×C271C2
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C8×C271, C3×C42×C271, C22×C3×C4×C271, …
maximal normal subgroup ofC2×C3×C8×C271, C3×C42×C271, C22×C3×C4×C271, …
maximal quotient ofC2×C3×C8×C271, C3×C42×C271, C22×C3×C4×C271, …
automorphism group ofC5×C1627, C3×C3253
outer automorphism group ofC5×C1627, C3×C3253

GAP

Past the SmallGroups library coverage — no SmallGroups id.