Finite Group Databasebeta

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C22×C32×C4×C13×C16 #72206776

order29952
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 226492416
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C32×C4×C13×C16
multiplicative(ℤ/47005)ˣ, (ℤ/52377)ˣ, (ℤ/56049)ˣ, (ℤ/56763)ˣ, (ℤ/60333)ˣ, (ℤ/60435)ˣ, (ℤ/65728)ˣ, (ℤ/69836)ˣ, (ℤ/70336)ˣ, (ℤ/74732)ˣ, (ℤ/75712)ˣ, (ℤ/80444)ˣ, (ℤ/90432)ˣ, (ℤ/94010)ˣ, (ℤ/96084)ˣ, (ℤ/97344)ˣ, (ℤ/103428)ˣ, (ℤ/104754)ˣ, (ℤ/112098)ˣ, (ℤ/113526)ˣ, (ℤ/120666)ˣ, (ℤ/120870)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C24×C32×C13
socle, prime radicalC24×C32×C13C2×C8
LCSG ▷ C1
UCSC1 ◁ G

6132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

29952 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.