Finite Group Databasebeta

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C22×C27×C32 #72183110

order3456
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 27648
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C27×C32
multiplicative(ℤ/10368)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9×C16C23×C3
socle, prime radicalC23×C3C9×C16
LCSG ▷ C1
UCSC1 ◁ G

240 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C27×C64, C2×C4×C27×C32, C23×C27×C32, …
maximal normal subgroup ofC22×C27×C64, C2×C4×C27×C32, C23×C27×C32, …
maximal quotient ofC22×C27×C64, C2×C4×C27×C32, C23×C27×C32, …
automorphism group ofC81×C128
outer automorphism group ofC81×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.