Finite Group Databasebeta

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C22×C3×C82×C13 #72188649

order9984
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 56623104
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C8

Aliases

abelianC22×C3×C82×C13
multiplicative(ℤ/30048)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C24×C3×C13
socle, prime radicalC24×C3×C13C42
LCSG ▷ C1
UCSC1 ◁ G

2684 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C13×C16, C2×C3×C4×C82×C13, C23×C3×C82×C13, …
maximal normal subgroup ofC22×C3×C8×C13×C16, C2×C3×C4×C82×C13, C23×C3×C82×C13, …
maximal quotient ofC22×C3×C8×C13×C16, C2×C3×C4×C82×C13, C23×C3×C82×C13, …
automorphism group ofC3×C32×C313
outer automorphism group ofC3×C32×C313

GAP

Past the SmallGroups library coverage — no SmallGroups id.