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C23×C3×C4×C5×C23 #72189587

order11040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3784704
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C4×C5×C23
multiplicative(ℤ/18095)ˣ, (ℤ/20163)ˣ, (ℤ/21855)ˣ, (ℤ/22935)ˣ, (ℤ/22936)ˣ, (ℤ/23265)ˣ, (ℤ/23312)ˣ, (ℤ/24376)ˣ, (ℤ/24464)ˣ, (ℤ/24675)ˣ, (ℤ/25816)ˣ, (ℤ/26884)ˣ, (ℤ/27640)ˣ, (ℤ/27800)ˣ, (ℤ/29140)ˣ, (ℤ/30580)ˣ, (ℤ/32900)ˣ, (ℤ/33144)ˣ, (ℤ/33168)ˣ, (ℤ/33192)ˣ, (ℤ/34404)ˣ, (ℤ/36190)ˣ, (ℤ/36564)ˣ, (ℤ/38724)ˣ, (ℤ/40326)ˣ, (ℤ/41460)ˣ, (ℤ/41700)ˣ, (ℤ/42300)ˣ, (ℤ/43710)ˣ, (ℤ/45870)ˣ, (ℤ/46530)ˣ, (ℤ/49350)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C5×C23
socle, prime radicalC24×C3×C5×C23C2
LCSG ▷ C1
UCSC1 ◁ G

944 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C5×C8×C23, C22×C3×C42×C5×C23, C24×C3×C4×C5×C23
maximal normal subgroup ofC23×C3×C5×C8×C23, C22×C3×C42×C5×C23, C24×C3×C4×C5×C23
maximal quotient ofC23×C3×C5×C8×C23, C22×C3×C42×C5×C23, C24×C3×C4×C5×C23
automorphism group ofC8×C47×C61, C16×C31×C47, C8×C11×C277, …
outer automorphism group ofC8×C47×C61, C16×C31×C47, C8×C11×C277, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.