Finite Group Databasebeta

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C24×C3×C49 #72182297

order2352
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1693440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C3×C49
multiplicative(ℤ/8232)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C24×C3×C7
socle, prime radicalC24×C3×C7C7
LCSG ▷ C1
UCSC1 ◁ G

402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C49, C25×C3×C49, C24×C9×C49, …
maximal normal subgroup ofC23×C3×C4×C49, C25×C3×C49, C24×C9×C49, …
maximal quotient ofC23×C3×C4×C49, C25×C3×C49, C24×C9×C49, …
automorphism group ofC3×C8×C343
outer automorphism group ofC3×C8×C343

GAP

Past the SmallGroups library coverage — no SmallGroups id.