Finite Group Databasebeta

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C3×C4×C25×C32 #72188302

order9600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 20480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C25×C32
multiplicative(ℤ/9797)ˣ, (ℤ/12125)ˣ, (ℤ/19594)ˣ, (ℤ/24250)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5×C16C22×C3×C5
socle, prime radicalC22×C3×C5C2×C5×C16
LCSG ▷ C1
UCSC1 ◁ G

216 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 ofC3×C4×C25×C64, C3×C8×C25×C32, C2×C3×C4×C25×C32, …
maximal normal subgroup ofC3×C4×C25×C64, C3×C8×C25×C32, C2×C3×C4×C25×C32, …
maximal quotient ofC3×C4×C25×C64, C3×C8×C25×C32, C2×C3×C4×C25×C32, …
automorphism group ofC97×C101, C2×C97×C125
outer automorphism group ofC97×C101, C2×C97×C125

GAP

Past the SmallGroups library coverage — no SmallGroups id.