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C22×C3×C4×C13×C23 #72192513

order14352
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 101376
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C13×C23
multiplicative(ℤ/17437)ˣ, (ℤ/18565)ˣ, (ℤ/20965)ˣ, (ℤ/22101)ˣ, (ℤ/22137)ˣ, (ℤ/22419)ˣ, (ℤ/23361)ˣ, (ℤ/23829)ˣ, (ℤ/26955)ˣ, (ℤ/29468)ˣ, (ℤ/29516)ˣ, (ℤ/31148)ˣ, (ℤ/31772)ˣ, (ℤ/34874)ˣ, (ℤ/37130)ˣ, (ℤ/41930)ˣ, (ℤ/44202)ˣ, (ℤ/44274)ˣ, (ℤ/44838)ˣ, (ℤ/46722)ˣ, (ℤ/47658)ˣ, (ℤ/53910)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C13×C23
socle, prime radicalC23×C3×C13×C23C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C42×C13×C23, C22×C3×C8×C13×C23, C23×C3×C4×C13×C23
maximal normal subgroup ofC2×C3×C42×C13×C23, C22×C3×C8×C13×C23, C23×C3×C4×C13×C23
maximal quotient ofC2×C3×C42×C13×C23, C22×C3×C8×C13×C23, C23×C3×C4×C13×C23
automorphism group ofC7×C47×C53, C5×C47×C79
outer automorphism group ofC7×C47×C53, C5×C47×C79

GAP

Past the SmallGroups library coverage — no SmallGroups id.