Finite Group Databasebeta

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C22×C3×C5×C128 #72186591

order7680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49152
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C5×C128
multiplicative(ℤ/13461)ˣ, (ℤ/15872)ˣ, (ℤ/17948)ˣ, (ℤ/23076)ˣ, (ℤ/26922)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC64C23×C3×C5
socle, prime radicalC23×C3×C5C64
LCSG ▷ C1
UCSC1 ◁ G

328 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C5×C256, C2×C3×C4×C5×C128, C23×C3×C5×C128, …
maximal normal subgroup ofC22×C3×C5×C256, C2×C3×C4×C5×C128, C23×C3×C5×C128, …
maximal quotient ofC22×C3×C5×C256, C2×C3×C4×C5×C128, C23×C3×C5×C128, …
automorphism group ofC31×C512
outer automorphism group ofC31×C512

GAP

Past the SmallGroups library coverage — no SmallGroups id.