Finite Group Databasebeta

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C2×C4×C27×C47 #72188776

order10152
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6624
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4×C27×C47
multiplicative(ℤ/12695)ˣ, (ℤ/15231)ˣ, (ℤ/20308)ˣ, (ℤ/25390)ˣ, (ℤ/30462)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C9C22×C3×C47
socle, prime radicalC22×C3×C47C2×C9
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10152 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C8×C27×C47, C42×C27×C47, C22×C4×C27×C47, …
maximal normal subgroup ofC2×C8×C27×C47, C42×C27×C47, C22×C4×C27×C47, …
maximal quotient ofC2×C8×C27×C47, C42×C27×C47, C22×C4×C27×C47, …
automorphism group ofC5×C2539
outer automorphism group ofC5×C2539

GAP

Past the SmallGroups library coverage — no SmallGroups id.