Finite Group Databasebeta

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C22×C4×C5×C103 #72187180

order8240
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 78336
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C103
multiplicative(ℤ/15465)ˣ, (ℤ/16496)ˣ, (ℤ/20620)ˣ, (ℤ/30930)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C5×C103
socle, prime radicalC23×C5×C103C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8240 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C8×C103, C2×C42×C5×C103, C23×C4×C5×C103, …
maximal normal subgroup ofC22×C5×C8×C103, C2×C42×C5×C103, C23×C4×C5×C103, …
maximal quotient ofC22×C5×C8×C103, C2×C42×C5×C103, C23×C4×C5×C103, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.