Finite Group Databasebeta

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C2×C4×C5×C8×C27 #72187491

order8640
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 147456
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C5×C8×C27
multiplicative(ℤ/13407)ˣ, (ℤ/16605)ˣ, (ℤ/17312)ˣ, (ℤ/17876)ˣ, (ℤ/26814)ˣ, (ℤ/33210)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4×C9C23×C3×C5
socle, prime radicalC23×C3×C5C2×C4×C9
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C5×C16×C27, C2×C5×C82×C27, C42×C5×C8×C27, …
maximal normal subgroup ofC2×C4×C5×C16×C27, C2×C5×C82×C27, C42×C5×C8×C27, …
maximal quotient ofC2×C4×C5×C16×C27, C2×C5×C82×C27, C42×C5×C8×C27, …
automorphism group ofC5×C41×C81
outer automorphism group ofC5×C41×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.