Finite Group Databasebeta

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C22×C3×C25×C32 #72188304

order9600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 61440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C25×C32
multiplicative(ℤ/19328)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5×C16C23×C3×C5
socle, prime radicalC23×C3×C5C5×C16
LCSG ▷ C1
UCSC1 ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C25×C64, C2×C3×C4×C25×C32, C23×C3×C25×C32, …
maximal normal subgroup ofC22×C3×C25×C64, C2×C3×C4×C25×C32, C23×C3×C25×C32, …
maximal quotient ofC22×C3×C25×C64, C2×C3×C4×C25×C32, C23×C3×C25×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.