Finite Group Databasebeta

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C22×C32×C52×C8 #72186270

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8847360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3×C5

Aliases

abelianC22×C32×C52×C8
multiplicative(ℤ/8897)ˣ, (ℤ/11439)ˣ, (ℤ/17794)ˣ, (ℤ/22878)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C32×C52
socle, prime radicalC23×C32×C52C4
LCSG ▷ C1
UCSC1 ◁ G

1824 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 ofC22×C32×C52×C16, C2×C32×C4×C52×C8, C23×C32×C52×C8, …
maximal normal subgroup ofC22×C32×C52×C16, C2×C32×C4×C52×C8, C23×C32×C52×C8, …
maximal quotient ofC22×C32×C52×C16, C2×C32×C4×C52×C8, C23×C32×C52×C8, …
automorphism group ofC7×C31×C41
outer automorphism group ofC7×C31×C41

GAP

Past the SmallGroups library coverage — no SmallGroups id.