Finite Group Databasebeta

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C2×C32×C52×C16 #72186261

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 737280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3×C5

Aliases

abelianC2×C32×C52×C16
multiplicative(ℤ/7471)ˣ, (ℤ/14942)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C32×C52
socle, prime radicalC22×C32×C52C8
LCSG ▷ C1
UCSC1 ◁ G

672 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C52×C32, C32×C4×C52×C16, C22×C32×C52×C16, …
maximal normal subgroup ofC2×C32×C52×C32, C32×C4×C52×C16, C22×C32×C52×C16, …
maximal quotient ofC2×C32×C52×C32, C32×C4×C52×C16, C22×C32×C52×C16, …
automorphism group ofC31×C241
outer automorphism group ofC31×C241

GAP

Past the SmallGroups library coverage — no SmallGroups id.