Finite Group Databasebeta

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C24×C52×C27 #72189357

order10800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 174182400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C5

Aliases

abelianC24×C52×C27
multiplicative(ℤ/23848)ˣ, (ℤ/35772)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C24×C3×C52
socle, prime radicalC24×C3×C52C9
LCSG ▷ C1
UCSC1 ◁ G

2144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C52×C27, C25×C52×C27, C24×C52×C81, …
maximal normal subgroup ofC23×C4×C52×C27, C25×C52×C27, C24×C52×C81, …
maximal quotient ofC23×C4×C52×C27, C25×C52×C27, C24×C52×C81, …
automorphism group ofC8×C11×C271
outer automorphism group ofC8×C11×C271

GAP

Past the SmallGroups library coverage — no SmallGroups id.