Finite Group Databasebeta

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C32×C5×C8×C13 #72184152

order4680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9216
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC32×C5×C8×C13

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C2×C32×C5×C13
socle, prime radicalC2×C32×C5×C13C4
LCSG ▷ C1
UCSC1 ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×C13×C16, C2×C32×C5×C8×C13, C3×C5×C8×C9×C13, …
maximal normal subgroup ofC32×C5×C13×C16, C2×C32×C5×C8×C13, C3×C5×C8×C9×C13, …
maximal quotient ofC32×C5×C13×C16, C2×C32×C5×C8×C13, C3×C5×C8×C9×C13, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.