Finite Group Databasebeta

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C22×C7×C17×C32 #72193249

order15232
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 147456
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C7×C17×C32
multiplicative(ℤ/30592)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C23×C7×C17
socle, prime radicalC23×C7×C17C16
LCSG ▷ C1
UCSC1 ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C7×C17×C64, C2×C4×C7×C17×C32, C23×C7×C17×C32
maximal normal subgroup ofC22×C7×C17×C64, C2×C4×C7×C17×C32, C23×C7×C17×C32
maximal quotient ofC22×C7×C17×C64, C2×C4×C7×C17×C32, C23×C7×C17×C32

GAP

Past the SmallGroups library coverage — no SmallGroups id.