Finite Group Databasebeta

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C2×C4×C52×C27 #72184705

order5400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 69120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC2×C4×C52×C27
multiplicative(ℤ/5951)ˣ, (ℤ/6775)ˣ, (ℤ/11902)ˣ, (ℤ/13550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C22×C3×C52
socle, prime radicalC22×C3×C52C2×C9
LCSG ▷ C1
UCSC1 ◁ G

256 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C52×C8×C27, C42×C52×C27, C22×C4×C52×C27, …
maximal normal subgroup ofC2×C52×C8×C27, C42×C52×C27, C22×C4×C52×C27, …
maximal quotient ofC2×C52×C8×C27, C42×C52×C27, C22×C4×C52×C27, …
automorphism group ofC11×C541, C25×C271
outer automorphism group ofC11×C541, C25×C271

GAP

Past the SmallGroups library coverage — no SmallGroups id.