Finite Group Databasebeta

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C2×C32×C4×C52×C8 #72192561

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 47185920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4×C5

Aliases

abelianC2×C32×C4×C52×C8
multiplicative(ℤ/16523)ˣ, (ℤ/17507)ˣ, (ℤ/22509)ˣ, (ℤ/33046)ˣ, (ℤ/35014)ˣ, (ℤ/45018)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C32×C52
socle, prime radicalC23×C32×C52C2×C4
LCSG ▷ C1
UCSC1 ◁ G

3888 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C4×C52×C16, C2×C32×C52×C82, C32×C42×C52×C8, …
maximal normal subgroup ofC2×C32×C4×C52×C16, C2×C32×C52×C82, C32×C42×C52×C8, …
maximal quotient ofC2×C32×C4×C52×C16, C2×C32×C52×C82, C32×C42×C52×C8, …
automorphism group ofC13×C31×C41, C7×C41×C61
outer automorphism group ofC13×C31×C41, C7×C41×C61

GAP

Past the SmallGroups library coverage — no SmallGroups id.