Finite Group Databasebeta

← Prev (#72186991) Next (#72186993) →

C22×C3×C25×C27 #72186992

order8100
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 38880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C25×C27
multiplicative(ℤ/12231)ˣ, (ℤ/24462)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5×C9C22×C32×C5
socle, prime radicalC22×C32×C5C5×C9
LCSG ▷ C1
UCSC1 ◁ G

210 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8100 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C25×C27, C23×C3×C25×C27, C22×C3×C25×C81, …
maximal normal subgroup ofC2×C3×C4×C25×C27, C23×C3×C25×C27, C22×C3×C25×C81, …
maximal quotient ofC2×C3×C4×C25×C27, C23×C3×C25×C27, C22×C3×C25×C81, …
automorphism group ofC2×C81×C151
outer automorphism group ofC2×C81×C151

GAP

Past the SmallGroups library coverage — no SmallGroups id.