Finite Group Databasebeta

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C2×C3×C42×C73 #72186092

order7008
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 221184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C73
multiplicative(ℤ/10255)ˣ, (ℤ/11427)ˣ, (ℤ/13155)ˣ, (ℤ/13185)ˣ, (ℤ/14032)ˣ, (ℤ/15236)ˣ, (ℤ/17540)ˣ, (ℤ/20510)ˣ, (ℤ/22854)ˣ, (ℤ/26310)ˣ, (ℤ/26370)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C73
socle, prime radicalC23×C3×C73C22
LCSG ▷ C1
UCSC1 ◁ G

216 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 ofC2×C3×C4×C8×C73, C3×C43×C73, C22×C3×C42×C73, …
maximal normal subgroup ofC2×C3×C4×C8×C73, C3×C43×C73, C22×C3×C42×C73, …
maximal quotient ofC2×C3×C4×C8×C73, C3×C43×C73, C22×C3×C42×C73, …
automorphism group ofC5×C7×C293, C3×C13×C293
outer automorphism group ofC5×C7×C293, C3×C13×C293

GAP

Past the SmallGroups library coverage — no SmallGroups id.