Finite Group Databasebeta

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C22×C7×C8×C73 #72194273

order16352
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 165888
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C7×C8×C73

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C7×C73
socle, prime radicalC23×C7×C73C4
LCSG ▷ C1
UCSC1 ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C7×C16×C73, C2×C4×C7×C8×C73, C23×C7×C8×C73
maximal normal subgroup ofC22×C7×C16×C73, C2×C4×C7×C8×C73, C23×C7×C8×C73
maximal quotient ofC22×C7×C16×C73, C2×C4×C7×C8×C73, C23×C7×C8×C73

GAP

Past the SmallGroups library coverage — no SmallGroups id.