Finite Group Databasebeta

← Prev (#72186264) Next (#72186266) →

C32×C4×C52×C8 #72186265

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2949120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4×C5

Aliases

abelianC32×C4×C52×C8

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C32×C52
socle, prime radicalC22×C32×C52C2×C4
LCSG ▷ C1
UCSC1 ◁ G

1056 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 ofC32×C4×C52×C16, C32×C52×C82, C2×C32×C4×C52×C8, …
maximal normal subgroup ofC32×C4×C52×C16, C32×C52×C82, C2×C32×C4×C52×C8, …
maximal quotient ofC32×C4×C52×C16, C32×C52×C82, C2×C32×C4×C52×C8, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.