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C22×C3×C5×C256 #72193345

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 98304
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C5×C256
multiplicative(ℤ/19789)ˣ, (ℤ/23901)ˣ, (ℤ/25377)ˣ, (ℤ/25443)ˣ, (ℤ/31744)ˣ, (ℤ/31868)ˣ, (ℤ/33836)ˣ, (ℤ/39578)ˣ, (ℤ/47802)ˣ, (ℤ/50754)ˣ, (ℤ/50886)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC128C23×C3×C5
socle, prime radicalC23×C3×C5C128
LCSG ▷ C1
UCSC1 ◁ G

372 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C512, C23×C3×C5×C256, C2×C3×C4×C5×C256
maximal normal subgroup ofC22×C3×C5×C512, C23×C3×C5×C256, C2×C3×C4×C5×C256
maximal quotient ofC22×C3×C5×C512, C23×C3×C5×C256, C2×C3×C4×C5×C256
automorphism group ofC7×C11×C257, C31×C1024
outer automorphism group ofC7×C11×C257, C31×C1024

GAP

Past the SmallGroups library coverage — no SmallGroups id.