Finite Group Databasebeta

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C22×C3×C8×C64 #72185308

order6144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 25165824
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C8

Aliases

abelianC22×C3×C8×C64
multiplicative(ℤ/18528)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C32C24×C3
socle, prime radicalC24×C3C4×C32
LCSG ▷ C1
UCSC1 ◁ G

3088 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C128, C22×C3×C16×C64, C2×C3×C4×C8×C64, …
maximal normal subgroup ofC22×C3×C8×C128, C22×C3×C16×C64, C2×C3×C4×C8×C64, …
maximal quotient ofC22×C3×C8×C128, C22×C3×C16×C64, C2×C3×C4×C8×C64, …
automorphism group ofC3×C32×C193
outer automorphism group ofC3×C32×C193

GAP

Past the SmallGroups library coverage — no SmallGroups id.