Finite Group Databasebeta

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C2×C4×C23×C27 #72184342

order4968
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3168
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C23×C27
multiplicative(ℤ/5123)ˣ, (ℤ/10246)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C22×C3×C23
socle, prime radicalC22×C3×C23C2×C9
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C8×C23×C27, C42×C23×C27, C22×C4×C23×C27, …
maximal normal subgroup ofC2×C8×C23×C27, C42×C23×C27, C22×C4×C23×C27, …
maximal quotient ofC2×C8×C23×C27, C42×C23×C27, C22×C4×C23×C27, …
automorphism group ofC47×C109, C2×C47×C109
outer automorphism group ofC47×C109, C2×C47×C109

GAP

Past the SmallGroups library coverage — no SmallGroups id.