Finite Group Databasebeta

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C24×C4×C13×C17 #72192309

order14144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1981808640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C4×C13×C17
multiplicative(ℤ/53160)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C13×C17
socle, prime radicalC25×C13×C17C2
LCSG ▷ C1
UCSC1 ◁ G

2724 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C8×C13×C17, C23×C42×C13×C17, C25×C4×C13×C17
maximal normal subgroup ofC24×C8×C13×C17, C23×C42×C13×C17, C25×C4×C13×C17
maximal quotient ofC24×C8×C13×C17, C23×C42×C13×C17, C25×C4×C13×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.