Finite Group Databasebeta

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C32×C4×C52×C16 #72192549

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5898240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C4×C5

Aliases

abelianC32×C4×C52×C16
multiplicative(ℤ/14701)ˣ, (ℤ/29402)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C32×C52
socle, prime radicalC22×C32×C52C2×C8
LCSG ▷ C1
UCSC1 ◁ G

1392 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 ofC32×C4×C52×C32, C32×C52×C8×C16, C2×C32×C4×C52×C16
maximal normal subgroup ofC32×C4×C52×C32, C32×C52×C8×C16, C2×C32×C4×C52×C16
maximal quotient ofC32×C4×C52×C32, C32×C52×C8×C16, C2×C32×C4×C52×C16
automorphism group ofC61×C241
outer automorphism group ofC61×C241

GAP

Past the SmallGroups library coverage — no SmallGroups id.