Finite Group Databasebeta

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C22×C4×C5×C7×C17 #72188262

order9520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 73728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C5×C7×C17
multiplicative(ℤ/13145)ˣ, (ℤ/17925)ˣ, (ℤ/19048)ˣ, (ℤ/23900)ˣ, (ℤ/26290)ˣ, (ℤ/28572)ˣ, (ℤ/35850)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C5×C7×C17
socle, prime radicalC23×C5×C7×C17C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C5×C7×C8×C17, C2×C42×C5×C7×C17, C23×C4×C5×C7×C17, …
maximal normal subgroup ofC22×C5×C7×C8×C17, C2×C42×C5×C7×C17, C23×C4×C5×C7×C17, …
maximal quotient ofC22×C5×C7×C8×C17, C2×C42×C5×C7×C17, C23×C4×C5×C7×C17, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.