Finite Group Databasebeta

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C22×C5×C7×C64 #72187756

order8960
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 73728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C5×C7×C64
multiplicative(ℤ/14817)ˣ, (ℤ/18176)ˣ, (ℤ/19756)ˣ, (ℤ/29634)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C23×C5×C7
socle, prime radicalC23×C5×C7C32
LCSG ▷ C1
UCSC1 ◁ G

284 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C7×C128, C2×C4×C5×C7×C64, C23×C5×C7×C64, …
maximal normal subgroup ofC22×C5×C7×C128, C2×C4×C5×C7×C64, C23×C5×C7×C64, …
maximal quotient ofC22×C5×C7×C128, C2×C4×C5×C7×C64, C23×C5×C7×C64, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.