Finite Group Databasebeta

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C24×C4×C5×C16 #72184471

order5120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1352914698240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C214×C4

Aliases

abelianC24×C4×C5×C16
multiplicative(ℤ/22440)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C26×C5
socle, prime radicalC26×C5C2×C8
LCSG ▷ C1
UCSC1 ◁ G

50986 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C4×C5×C32, C24×C5×C8×C16, C23×C42×C5×C16, …
maximal normal subgroup ofC24×C4×C5×C32, C24×C5×C8×C16, C23×C42×C5×C16, …
maximal quotient ofC24×C4×C5×C32, C24×C5×C8×C16, C23×C42×C5×C16, …
automorphism group ofC3×C5×C8×C11×C17
outer automorphism group ofC3×C5×C8×C11×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.