Finite Group Databasebeta

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C2×C3×C27×C32 #72184520

order5184
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 20736
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C3×C27×C32
multiplicative(ℤ/7857)ˣ, (ℤ/15714)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9×C16C22×C32
socle, prime radicalC22×C32C9×C16
LCSG ▷ C1
UCSC1 ◁ G

238 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C27×C64, C3×C4×C27×C32, C22×C3×C27×C32, …
maximal normal subgroup ofC2×C3×C27×C64, C3×C4×C27×C32, C22×C3×C27×C32, …
maximal quotient ofC2×C3×C27×C64, C3×C4×C27×C32, C22×C3×C27×C32, …
automorphism group ofC81×C97, C2×C81×C97
outer automorphism group ofC81×C97, C2×C81×C97

GAP

Past the SmallGroups library coverage — no SmallGroups id.