Finite Group Databasebeta

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C22×C3×C8×C73 #72186093

order7008
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 55296
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C8×C73
multiplicative(ℤ/14024)ˣ, (ℤ/14048)ˣ, (ℤ/21036)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C3×C73
socle, prime radicalC23×C3×C73C4
LCSG ▷ C1
UCSC1 ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7008 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C16×C73, C2×C3×C4×C8×C73, C23×C3×C8×C73, …
maximal normal subgroup ofC22×C3×C16×C73, C2×C3×C4×C8×C73, C23×C3×C8×C73, …
maximal quotient ofC22×C3×C16×C73, C2×C3×C4×C8×C73, C23×C3×C8×C73, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.